Klecko was drafted by the New York Jets in the sixth round (144th overall) of the 1977 NFL Draft. Despite eight sacks by Klecko, his team went only 3–11 his first season. However, when he and Abdul Salaam were joined by Mark Gastineau and Marty Lyons on the Jets' defensive line, they formed one of the top defensive lines in the NFL, known as the "New York Sack Exchange." The four combined for 66 sacks in 1981, including a league-leading 20.5 by Klecko, to lead the Jets to their first playoff game since 1969. Klecko was honored with his first All-Pro selection. In November 1981, Klecko, Gastineau, Salaam and Lyons were invited to ring the ceremonial opening bell at the New York Stock Exchange, which served as the inspiration for their nickname.