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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 Mark 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, and was named the NFL's Defensive Player of the Year by the Newspaper Enterprise Association (NEA).
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. Klecko was the second NFL player ever to be named to the Pro Bowl at three different positions (DE, NT and DT) and he was the NFL Defensive Player of the Year. Klecko remains one of the most popular Jets of all time. On December 26, 2004, the New York Jets honored Klecko when they retired his #73 jersey. He became only the third New York Jet to have his number retired, joining Hall of Fame QB Joe Namath and Hall of Fame WR Don Maynard.
Klecko and his wife, Debbie, currently reside in Colts Neck, New Jersey and have five children. One of whom, Dan, is an NFL defensive tackle. Though Klecko never made it to a Superbowl, his son has won three Superbowl rings.
Klecko currently fabricates metal stairs in the Tri-State Area, and serves as a representative for various construction companies. He had small roles in three Burt Reynolds films: Cannonball Run, Heat, and Smokey And The Bandit II. He also appeared on EWTN Life On The Rock show and his faith is very important to him. In September 2010, Sports Net New York announced that Klecko would be the newest analyst on the New York Jets post game show.