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 in the market and scavenge for food and water. She also helps care for a new 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 under Katende's guidance.
Over several years, her success in competitions and tournaments leads to higher-level competitions, stress, and identity issues. Phiona must learn more than the game as she is exposed to life outside Katwe. Her education, both formally and informally, continues as she dreams of gaining escape from poverty for herself, her mother and siblings.