Kočí was drafted 146th overall in the 2000 NHL Entry Draft by the Pittsburgh Penguins. Kočí played in the WHL with the Prince George Cougars in the 2000-01 season before turning professional for the 2001-02 season. Kočí spent the next five years with the Penguins minor-league affiliates, between the Wheeling Nailers of the ECHL and Wilkes-Barre/Scranton Penguins of the AHL. Prior to the 2006-07 season, Kočí signed with the Chicago Blackhawks on July 17, 2006. Kočí was assigned to the Blackhawks affiliate, the Norfolk Admirals, but made his NHL debut on March 10, 2007, against the Phoenix Coyotes, and amassed 32 penalty minutes in three fights. He lost his first fight to Josh Gratton, but managed to get a rematch in which he fared much better. He fought defenceman Nick Boynton as well. By the end of the 2006–07 season, David played in nine games and collected 88 penalty minutes. During the Blackhawks' loss to the Boston Bruins on October 25, 2007, Kočí got into one of the nastiest hockey brawls in recent hockey memory with Bruins defenceman Zdeno Chára. Kočí, who had broken his nose several days before, and Chára started punching each other; blood started to spatter from Kočí's nose. The Blackhawks placed Kočí on injured reserve and he missed about two weeks. On July 1, 2008, Kočí signed with the Tampa Bay Lightning to a one-year deal. During the 2008–09 season, on October 21, 2008, David was claimed off waivers by St. Louis Blues after only playing one game for Tampa Bay. Kočí then returned to the Lightning after he was placed on waivers after 4 games with the Blues. Kočí scored his first NHL goal in a 3-2 defeat against the Montreal Canadiens on March 26, 2009. The puck was actually tapped in by a Canadiens player but credit was given to him. On July 1, 2009, Kočí signed a one-year contract with the Colorado Avalanche. He scored his first goal with the Avalanche, and second career goal, when he unintentionally deflected in a Brett Clark shot in a 3-2 victory over the Calgary Flames on October 28, 2009. On December 15, 2009, during a 6-1 defeat to the Washington Capitals, Kočí raised ire after he was ejected from the game after a major boarding penalty on Capitals defenseman Mike Green. He was subsequently fined by the NHL. Kočí recorded 11 Fighting Majors before suffering a broken hand in a fight against D.J. King of the St. Louis Blues on February 8, 2010. He finished the 2009–10 season with a career-high 43 games and was re-signed to a one-year contract by the Avalanche on June 2, 2010. A free agent, on September 1, 2011, Koci was invited to the Winnipeg Jetstraining Camp before he was released prior to the 2011–12 season on September 30, 2011. In returning to his native Czech Republic, he linked up with his former youth club, HC Sparta Praha, and made his long-awaited Czech Extraliga debut. In leading Sparta with 132 penalty minutes, Koci also contributed with 5 assists, to earn a one-year extension with the club on May 21, 2012.
