The 22-year-old crashed in training and did not compete in Sochi four years ago as a result, belatedly making her Great Britain bow at the Phoenix Snow Park in Pyeongchang.
She scored 74.00 for her first of two qualification runs, good enough to advance as one of 12 qualifiers led by Cassie Sharpe of Canada, who was awarded a best of 93.40.
If Cheshire finishes on the podium on Tuesday, Team GB will reach the record medal target set by UK Sport at the beginning of the Games.
Dom Parsons won Britain's first medal of the Olympics, claiming bronze in the skeleton, before Lizzy Yarnold and Laura Deas took gold and bronze respectively in the same event.
Izzy Atkin also won bronze in the ski slopestyle and now Cheshire has the chance to help Britain meet their medal target of five.
When is Rowan Cheshire in action in Pyeongchang (UK times)?
Tuesday, Feb 20
Ski halfpipe final, run one
Ski halfpipe final, run two
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