Born in Indianapolis, Indiana, Kitchen was signed up for soccer by his mother and quickly excelled in the sport, as his local league made him play two age groups higher due to his ability. Two years later he was signed to the Chicago Magic, a team in the U.S. Soccer Development Academy, while remaining in Indiana. He was invited to spend two years in the United States men's national under-17 soccer team camp in Bradenton, Florida and captained the team at the 2009 FIFA U-17 World Cup in Nigeria. In 2010, he enrolled at University of Akron and played a season for the Akron Zips, who won the 2010 NCAA Division I Men's Soccer Championship under Caleb Porter with other future MLS players such as Darlington Nagbe. He started 25 games for the Zips in 2010, scoring six goals and adding one assist. He earned an All-MAC First Team selection and scored an unassisted goal on a right-footed blast from 30 yards out during Akron's 2–1 win over the Michigan Wolverines in the national semifinal of the College Cup. Kitchen also made a solitary appearance for USL Premier Development League club Chicago Fire Premier in 2010.
Professional career
D.C. United
Kitchen passed on a trial offer from Belgium's Anderlecht to sign a Generation Adidas contract with MLS. He was selected by D.C. United in the first round of the 2011 MLS SuperDraft. He made his professional debut on March 19, 2011 in United's 2011 MLS season opener against the Columbus Crew, and scored his first professional goal on May 29 in a 3-2 win over the Portland Timbers. Perry was a finalist for the 2011 Rookie of the Year award, although he was ultimately not selected. He recorded 4 assists for the season of 2013, which was the record high for the team that year. He was voted D.C. United's Most Valuable Player of the 2013 season. He played all five matches of their 2013 U.S. Open Cup win, including the 1–0 final victory at Real Salt Lake on October 1. Kitchen's deal with D.C. United expired after the 2015 season.
Europe
Kitchen signed with Heart of Midlothian on a -year deal on March 9, 2016. He made his debut in the Scottish Premiership three days later in a 1–0 win at Dundee, as a 73rd-minute substitute for Sam Nicholson. On September 21, 2016, Kitchen was appointed club captain. Kitchen played less often after Ian Cathro was appointed Hearts manager, and he was allowed to leave the club at the end of the season. Kitchen signed for Danish Superliga club Randers on a two-year deal in July 2017.
LA Galaxy
Kitchen returned to the United States when he signed with LA Galaxy in January 2018. LA acquired his MLS rights from D.C. United in exchange for $100,000 in general allocation money and $200,000 in targeted allocation money. He made his debut on March 4 in the season opener, a 2–1 win over Portland. The Galaxy missed the play-offs.
International
Kitchen, who captained the United States men's national under-17 soccer team at the 2009 FIFA U-17 World Cup in Nigeria, also played with the under-20 team. On January 9, 2015, Kitchen was called to the senior training camp for the first time. He made his first international appearance on February 8 that year against Panama at the StubHub Center, replacing the injured DeAndre Yedlin for the last 22 minutes of a 2–0 win. He was part of the 23-man squad that Jürgen Klinsmann called up for the Copa América Centenario on home soil in May 2016. The team came fourth, though he did not play.
