Living in Katwe, a slum in Kampala, Uganda, is a constant struggle for 10-year-old Phiona (Madina Nalwanga), her mother Nakku Harriet (Lupita Nyong'o) and younger members of her family. She and her younger brother help their mother sell maize in the market. She also helps care for her baby brother. Her world changes one day when she meets Robert Katende (David Oyelowo) at a missionary program. Katende coaches soccer and teaches children to play chess at a local center. Curious, Phiona approaches and learns the game. She becomes fascinated with it and soon becomes a top player in the group under Katende's guidance.
Her coach, over the initial opposition of the local chess authorities, takes her and the team to a national school level tournament at a prestigious local school. The group initially finds itself ill at ease among the other participants and the more affluent surroundings. However, their talent wins the day and Phiona comes in first place.
The film then proceeds to trace the ups and downs of success at competitions and tournaments for Phiona and her fellow Pioneers. The struggles of life in Katwe are ever present and Phiona hopes that chess will provide a means of escape from Katwe for her and her family.
Phiona leads the Uganda team at the Chess Olympiad in Russia, confident that she will succeed in becoming a Grand Master, securing the necessary finances to lift her family from poverty. However, the competition proves too tough, and she yields to her Canadian opponent.