From Christ Church Parish, Chase made his senior debut for Barbados during the 2010–11 Regional Four Day Competition, aged 18. After two matches in his debut season, he did not appear again until the 2012–13 competition, although he has since become a regular in the team. During the 2014–15 season, Chase scored a maiden first-class century, 120 not out from 241 balls against the Windward Islands. He finished the season with 534 runs from eight matches, which placed him fourth for Barbados and eighth in the overall competition. Chase continued his good form during the 2015–16 season, being named man of the match against the Leeward Islands after making 136 not out in his team's first innings.

In June 2018, he was named the Best Regional Limited-Overs Cricketer of the Year at the annual Cricket West Indies' Awards. Ahead of the 2018 Caribbean Premier League, he was named as one of five players to watch in the tournament.

In July 2016, he was named in the West Indies squad for their Test series against India.^[8] He made his Test debut for the West Indies on 21 July 2016.^[9] In his second Test match, Chase picked up his maiden five-wicket haul and scored a century to stave off a strong Indian bowling attack.^[10][11]

In June 2017, he was named in the West Indies One Day International (ODI) squad for their series against Afghanistan.^[12] He made his ODI debut for the West Indies against Afghanistan on 9 June 2017.^[13]