Funny thing, I seem to remember this story from TV, or the newspapers.  I remember the part where he was charged, or was going to be charged, with violating the airport's airspace…
 
Let's approach this as three sides to every story: yours, mine and the facts.
 
 
#1 - Yours: as Robert tells it.
 
Now let me tell you about Larry Walters, my hero.  Walters is a truck driver, thirty three years old.  He is sitting in his lawn chair in his backyard, wishing he could fly.  For as long as he could remember, he wanted to go up.  To be able to just rise right up in the air and see for a long way.  The time, money, education, and opportunity to be a pilot were not his.  Hang gliding was too dangerous, and any good place for gliding was too far away.  So he spent a lot of summer afternoons sitting in his backyard in his ordinary old aluminum lawn chair—the kind with the webbing and rivets.  Just like the one you've got in your backyard.
 
The next chapter in this story is carried by the newspapers and television.  There's old Larry Walters up in the air over Los Angeles.  Flying at last.  Really getting UP there.  Still sitting in his aluminum lawn chair, but it's hooked on to forty-five helium-filled surplus weather balloons.  Larry has a parachute on, a CB radio, a six-pack of beer, some peanut butter and jelly sandwiches, and a BB gun to pop some of the balloons to come down.  And instead of being just a couple of hundred feet over his neighborhood, he shot up eleven thousand feet, right through the approach corridor to the Los Angeles International Airport.
 
Walters is a taciturn man.  When asked by the press why he did it, he said, "You can't just sit there."  When asked if he was scared, he answered, "Wonderfully so."  When asked if he would do it again, he said, "Nope."  And asked if he was glad that he did it, he grinned from ear to ear and said, "Oh, yes."
 
The human race sits in its chair.  On the one hand is the message that says there's nothing left to do.  And the Larry Walterses of the earth are busy tying balloons to their chairs, directed by dreams and imagination to do their thing.
 
The human race sits in its chair.  On the one hand is the message that the human situation is hopeless.  And the Larry Walterses of the earth soar upward knowing anything is possible, sending back the message from eleven thousand feet: "I did it, I really did it.  I'm FLYING."
 
It's the spirit here that counts.  The time may be long, the vehicle may be strange or unexpected.  But if the dream is held close to the heart, and imagination is applied to what there is close at hand, everything is still possible.
 
© Robert Fulghum from "All I Really need to Know I Learned in Kindergarten"
 
 
#2 - Mine (if anybody cares!):  
 
Well, there are dreamers, and then, there are dreamers. Mother Teresa was a dreamer who not only found "God," but a way to make that belief count for all the years she served humanity.  She got a Nobel Peace Prize, though I'm sure it mattered little to her, and she probably had to be coaxed to accept it.  She didn't get a Darwin Award.  And she did not end up committing suicide. 
 
Walters' effort was notorious and created some laughter, and a bit of embarrassment to the bureaucracy and its ever growing contradictory rules, but it did not change anything that I can see.  It did not even change Walters.  Just a different approach to the Evel Knievel stunts with no better result.  
 
#3 - The Facts: (from Wikipedia)

Origin of his plan

Walters had always dreamed of flying, but was unable to become a pilot in the United States Air Force because of his poor eyesight. Walters had first thought of using weather balloons to fly at age 13, after seeing them hanging from the ceiling of a military surplus store. Twenty years later he decided to do so. His intention was to attach a few helium-filled weather balloons to his lawnchair, cut the anchor, and then float above his backyard at a height of about 30 feet (9.1 m) for several hours. He planned to use a pellet gun to burst balloons to float gently to the ground.
[edit] Preparation and launch

In mid-1982, Walters and his girlfriend, Carol Van Deusen, purchased 45 eight-foot weather balloons and obtained helium tanks from California Toy Time Balloons. They used a forged requisition from his employer, FilmFair Studios, saying the balloons were for a television commercial. Walters attached the balloons to his lawn chair, filled them with helium, put on a parachute, and strapped himself into the chair in the backyard of a home at 1633 W. 7th St. in San Pedro[2] He took his pellet gun, a CB radio, sandwiches, cold beer, and a camera. When his friends cut the cord that tied his lawn chair to his Jeep, Walters' lawn chair rose rapidly to a height of about 15,000 feet (4,600 m). At first, he did not dare shoot any balloons, fearing that he might unbalance the load and cause himself to spill out. He slowly drifted over Long Beach and crossed the primary approach corridor of Long Beach Airport.

He was in contact with REACT, a CB monitoring organization, who recorded their conversation:
REACT: What information do you wish me to tell [the airport] at this time as to your location and your difficulty?
Larry: Ah, the difficulty is, ah, this was an unauthorized balloon launch, and, uh, I know I'm in a federal airspace, and, uh, I'm sure my ground crew has alerted the proper authority. But, uh, just call them and tell them I'm okay.

After 45 minutes in the sky, he shot several balloons, and then accidentally dropped his pellet gun overboard. He descended slowly, until the balloons' dangling cables got caught in a power line, causing a blackout in a Long Beach neighborhood for 20 minutes. Walters was able to climb to the ground.
 
Arrest and notoriety

He was immediately arrested by waiting members of the Long Beach Police Department; when asked by a reporter why he had done it, Walters replied, "A man can't just sit around."
Regional safety inspector Neal Savoy was reported to have said, "We know he broke some part of the Federal Aviation Act, and as soon as we decide which part it is, some type of charge will be filed. If he had a pilot's license, we'd suspend that. But he doesn't." Walters was initially fined US$4,000 for violations under U. S. Federal Aviation Regulations, including operating an aircraft within an airport traffic area "without establishing and maintaining two-way communications with the control tower." Walters appealed, and the fine was reduced to US$1,500.[3] (A charge of operating a "civil aircraft for which there is not currently in effect an Airworthiness Certificate" was dropped, as it was not applicable to this class of aircraft.) Walters commented, "If the FAA was around when the Wright Brothers were testing their aircraft, they would never have been able to make their first flight at Kitty Hawk."
Walters received the top prize from the Bonehead Club of Dallas for his adventure, as well as invitations from The Tonight Show and Late Night with David Letterman, plus an honorable mention in 1982's Darwin Awards.

Walter's flight was replicated (though tethered) on one of the pilot episodes of the TV show MythBusters, in which one of the show's hosts was lifted to a height just under 30 m (100 ft) and gradually reduced his altitude by shooting balloons with a pellet gun.
Later years

The lawnchair used in the flight was given to an admiring boy named Jerry, though Walters later regretted doing so, since the Smithsonian Institution asked him to donate it to its museum. Twenty years later, Jerry, by then an adult, sent an e-mail to Mark Barry, a pilot who had documented Walters's story and dedicated a Web site to it, and identified himself. It was still sitting in his garage, attached to some of the original tethers and water jugs used as ballast.[4]

Walters said, "It was something I had to do. I had this dream for twenty years, and if I hadn't done it, I think I would have ended up in the funny farm. I didn't think that by fulfilling my goal in life — my dream — that I would create such a stir and make people laugh."

After his flight, he was in brief demand as a motivational speaker and he quit his job as a truck driver. He was featured in a Timex print ad in the early '90s,[5] but he never made much money from his fame. Later in his life, Walters hiked the San Gabriel Mountains and did volunteer work for the United States Forest Service. He later broke up with his girlfriend of 15 years and could only find work sporadically as a security guard.
He committed suicide in 1993 at the age of 44 by shooting himself in the heart in Angeles National Forest.