Chapman spent two years at TFC Academy, before leaving to play at Michigan State University. During his final year, Chapman was named as a First Team All-American, the first Spartan to achieve first team honours since 1970. Chapman was also a 2014 MAC Hermann Trophy semifinalist,[1] and Big Ten Midfielder of the Year.[2] In 2012, he signed with SC Toronto of the Canadian Soccer League, and made his debut on May 11, 2012, in a match against St. Catharines Wolves, and recorded his first goal for the club in a 5–0 victory.[3][4]
In 2013, Chapman made 14 appearances and scored three goals for K-W United in the PDL.[5]
On July 12, 2016, Chapman and teammate Jordan Hamilton were named to the 2016 Chipotle MLS Homegrown team as part of Major League Soccer's 2016 All Star Game festivities.[10]
On November 13, 2019, Chapman was traded to Inter Miami in exchange for $100,000 in General Allocation Money.[11] Following the 2021 season, Chapman's contract option was declined by Miami.[12]
In January 2022, Scottish Premiership club Dundee announced they had signed Chapman to a deal, subject to international clearance and a work permit.[13] Chapman would make his debut as a substitute in the Dundee derby on February 1.[14] Chapman would play once more for Dundee in a league game against Motherwell as he would struggle to break into the first team.[15][16] Chapman returned to North America at the end of the season, and despite being contracted for another year he did not return to Scotland, apparently due to "paperwork issues".[17] Chapman would officially leave Dundee by mutual consent in October.[18]
In November 2023, Chapman signed with Hartford Athletic of the USL Championship for the 2024 season.[20] He made his debut on March 9 in a league win over El Paso Locomotive.[21]