Chadwick began kart racing at the age of eleven, following her brother Oliver into the sport. She transitioned to car racing in 2013 after winning a scholarship at the Ginetta Junior Championship weekend, choosing the opportunity over a trial with the England under-eighteen hockey team. She spent two seasons in the Ginetta Junior Championship, finishing tenth in 2013 and eighth in 2014.
In 2015, Chadwick stepped up to the British GT Championship with Beechdean Motorsport, competing in the GT4 class in an Aston Martin V8 Vantage alongside co-driver Ross Gunn. The pairing took two wins and five podiums across the season, including victory in the Silverstone 24-Hour race. The result made Chadwick the first female and youngest-ever champion of the British GT Championship. She returned to the series in 2016 with two different outfits and also entered the 2016 VLN season at the Nürburgring, finishing third in class in her race.
In 2017, Chadwick moved into single-seater racing with Double R Racing in the BRDC British Formula 3 Championship, recording a third-place finish at Rockingham. For 2018, she moved to Douglas Motorsport and became the first woman ever to win a British F3 race, taking victory in the reversed-grid race at Brands Hatch.
She also competed in the 2018-19 MRF Challenge season, winning six of the final ten races at Bahrain and Chennai to claim the MRF Challenge title — becoming the first woman to win the series.
In 2018, she also entered the 24 Hours of Nürburgring alongside Jonathan Adam, Alex Lynn, and Pete Cate in an Aston Martin Vantage V8 GT4, finishing fifth in class.
Chadwick entered the inaugural W Series in 2019 and dominated the championship. She took the first-ever W Series race win at Hockenheim and won the title at the Brands Hatch finale, having led the championship throughout. The 2020 season was cancelled due to the COVID-19 pandemic.
In 2021, she retained her title after a closely fought season-long battle with Alice Powell. In 2022, driving for Jenner Racing, she won five consecutive W Series races including victories at the Miami International Autodrome and Circuit de Barcelona-Catalunya. After the 2022 season was terminated early for financial reasons, Chadwick was confirmed as champion for the third time, ahead of Beitske Visser.
On 20 May 2019, Chadwick joined the Williams Driver Academy as a development driver, becoming the second driver to join the programme. She remained with Williams in subsequent years and drove Keke Rosberg's FW08C at the 2023 Goodwood Festival of Speed, marking her first time in a Formula 1 car. By 2024, her title evolved to Williams Racing Driver, and she also took on an advisory role for the F1 Academy programme.
In December 2022, Andretti Autosport announced that Chadwick would compete in the 2023 Indy NXT season — the rebranded Indy Lights series. After a challenging debut year adapting to unfamiliar tracks and machinery, she improved noticeably in the second half of the season, taking five top-ten finishes in the final eight races.
Returning for the 2024 Indy NXT season with the rebranded Andretti Global team, Chadwick demonstrated clear progress. She finished on the podium at Indianapolis Motor Speedway, becoming the first woman to podium in Indy NXT since Pippa Mann in 2010. At Road America in race 6, she converted a maiden pole position into a maiden race victory, becoming the first woman to win in Indy NXT/Indy Lights since Mann in 2010 and the first woman in series history to claim both a road course pole and a road course win.
In December 2024, Chadwick signed with IDEC Sport for the 2025 European Le Mans Series season, partnering with Mathys Jaubert. The team operates in collaboration with Genesis Magma Racing as that organisation prepares for a Le Mans Hypercar entry in 2026.
Chadwick competed for Great Britain alongside David Coulthard in the Race of Champions. She raced in Extreme E in 2021 with Veloce Racing, finishing second in the second round of the series. She has also been involved with Jaguar Racing as a Formula E test driver, participating in the 2020 rookie test and the 2024-25 and 2025-26 women's and rookie tests.
Chadwick's career represents a series of barriers broken across multiple racing categories — in British GT, MRF Challenge, British Formula 3, W Series, and Indy NXT. Her ability to adapt across GT, single-seater, and endurance disciplines while accumulating championship wins has made her one of the most successful women in the history of motorsport.