Chapman signed for Chesterfield from nearby non-league side, Belper Town in the summer of 2013. On 23 September 2014, Chapman joined Accrington Stanley on a two-month loan deal. In summer 2016, Chapman joined Accrington Stanley on a two-year contract. Accrington Stanley won the League Two title in 2017–18, with Chapman also winning the League Two Golden Glove award, having kept 18 clean sheets in 45 league games. At the end of the season, he was offered a new contract. On 15 May 2018, Chapman joined Peterborough united, where he remained until he was released on 12 June 2020. On 7 October 2020, Chapman was announced as a new signing by Scottish Premiership club Motherwell, but in July 2021, Chapman returned to England to join League One side Gillingham following his release from Motherwell following their relegation. In May 2022, Chapman signed for Stevenage, but after finding limited opportunities to play, he signed for Scunthorpe United in February 2023.