20K Feet is no big feat (pun intended)
20K feet is no big deal for bailing out of high altitude aircraft; during WWII, it was a height that was quite normal for some bomber crews to bail out at. I wouldn't exactly say, therefore, that he "parachuted from space".
However, since you want to know, August 16, 1960 is the date when a US Air Force Officer "Jumped from Space", with an 102,800 ft jump (they used a balloon to get above the stratosphere). Nova had an interesting episode on back in 1999, and even put out a small little Windows program that allows you to recreate the ascent and jump. If you look for it, you might still be able to find it; it was called "Skydive from the Stratosphere"; it will run on Win95, Win98, Win98SE, WinNT, WinME, and it SHOULD run on the various Win2K and WinXP flavors. Perhaps you can get it from the PBS/WGBH website.
As for the "Astronaut" (Col Kittinger) who made the jump, he had to wear a pressure suit; he had a malfunction that caused the suit to lose pressure in one of the hands, while during the jump he nearly went supersonic before hitting his stablizing chute.
(Edit): I almost forgot! Initial accounts of the flight of Gargarin DID say that he parachuted out of the capsule; there is even a patriotic peace in Pravda of how, while swinging on the parachutes, Gargarin watched his capsule touch down, while singing patriotic Russian ballads. Pure propaganda, probably, but that was before the FAI was asked to qualify the record; as soon as someone realized that the FAI wouldn't qualify the record, the account suddenly changed. Even then, however, a distant echo cropped back up (here's REAL trivia for you!) in the accounts of Valentina Tereshkova, the first woman to fly into space; she had been one of the seamstresses who had sewn the egress parachutes for the Vostok capsules (she flew more as a public relations event than anything else). During her briefings, she talked about how proud she was to know that Gargarin and all the other Cosmonauts were using parachutes that she and her coworkers had made.
A great source for early Soviet Space Shots is "Red Star in Orbit", by James Oberg.
