Chulk played baseball at the Perrine Khoury League throughout much of his childhood, and graduated in 1996 from Miami Palmetto Senior High School. That year, he was named MVP and received Best Pitcher Award. He defeated the Southridge Spartans during the playoffs in 1996, the team that had cut him the year prior. He attended St. Thomas University in Miami, where he graduated in 2000, majoring in Sports Management. Chulk played college baseball and received Best Pitcher Award of the Sun Conference in 1998, 1999, 2000 and the Regional Pitcher of the Year Award in his senior year.

Before Chulk was traded to the San Francisco Giants in the National League, he played for the Toronto Blue Jays of the American League from 2003 to 2006. On July 21, 2006, he was traded by Toronto to San Francisco with Shea Hillenbrand in exchange for reliever Jeremy Accardo. He was designated for assignment by the Giants on June 24, 2008. He became a free agent at the end of the season.

Chulk signed a minor league contract with the Cleveland Indians on January 15, 2009. The deal was finalized in February. The Indians purchased his contract and added him to the roster on April 11. On May 6, Chulk was designated for assignment. He cleared waivers and accepted a minor league assignment to Triple-A affiliate Columbus Clippers. In October 2009, Chulk was granted free agency.

He was signed to a minor league contract by the Pittsburgh Pirates on December 7, 2009.

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