By the time Klíma was 20 years old, officials on his Dukla Jihlava team knew that the Detroit Red Wings were eager to bring the young star to the NHL. Rumors were rampant that the Wings were trying to pay off Czechoslovak authorities to get Klíma out of his native country, but despite all the hype that surrounded him, Czechoslovak hockey authorities made no real effort to clamp down and prevent Klíma from traveling in Europe. As a result, Klíma managed to defect to North America during the summer of 1985, making him the first Czech player to defect directly to a U.S.-based team rather than one of the NHL's Canadian teams which had smuggled several Czechs and Slovaks out of Europe in the past.