Cut the chicken breast fillets into bite-sized pieces.
Heat the olive oil in a non-stick pan over medium heat. Add the onion and garlic, stirring constantly, until the onion is golden brown (about 5 minutes). Transfer to a plate.
Put the chicken pieces in the same pan and stir-fry for about 5 minutes until lightly browned on the outside.
Add the tomatoes, mushrooms, white wine, salt, and pepper. Return the onions and garlic to the pan and stir well. Bring to a boil, then reduce heat to low and simmer for about 15 minutes until the liquid has reduced by roughly half and the chicken reaches 74°C (165°F) internally.
Add the basil strips, stir well, then remove from heat and let steep for 1 to 2 minutes.