Since the Chicago Blackhawks are an original 6 team, they have been participating in drafts of one form or another since 1963. Their first ever pick was 5th overall in the 1963 Amateur draft when they struck out by selecting Art Hampson. Art would not ever play an NHL game, and I know very little of what became of Art. The Blackhawks would not have any success with their selections for the next several Amateur drafts before getting a hit in 1968 with John Marks, a defenceman from Winnipeg Manitoba.
Chicago's greatest draft success came in the 1980 NHL Entry Draft.
What is amazing about this draft is not only do they score one of the most exciting players to watch in NHL history with their first pick, they continue the draft selecting 8 more players that would eventually make the NHL. Ludzik, Murray, Wilson and Larmer would all go on to play over 400 NHL games a piece and of course Larmer would be an offensive superstar in his own right scoring 441 career goals while averaging more than a point a game in his 1000+ game NHL career. Denis Savard was the gem of the draft for the Hawks where he would break 100+ points 5 times for the Blackhawks during the 80's. Unfortunately for Blackhawks fans, Savard would leave Chicago and go on to win a Stanley Cup in a different uniform.
If you ignore the tiny 3 to 4 round Amateur drafts during the 60's then the worst draft in Chicago history would be the 1989 Entry Draft.
With the 6th overall selection in the draft, Chicago selected Adam Bennett. By selecting Bennett, the Hawks missed out on great 2-way forwards like Holik and Sillinger who were taken later than first round. Bennett who played a total of 69 games was by far the best Hawks selection in the draft. Only Tichy would ever play in the NHL from the remaining 9 selections Chicago had in the draft. Some other missed talent was: Nick Lidstrom, Patrice Brisebois, Robert Reichel, Sergei Fedorov and Pavel Bure.