Chop chicken breast into small bite-size pieces. Add to a bowl along with the salt, pepper, and flour. Toss to coat the chicken in the flour.
Heat a large skillet over medium heat. Heat the oil and add the chicken. Reserve the flour left in the bowl.
Cook the chicken for about 5 minutes until browned. Remove the chicken from the skillet. If the skillet looks dry, add a bit more oil.
Add the onion and cook for 5 minutes or until it begins to soften. Add garlic and ginger and cook for 1 minute longer. Add the reserved flour and stir until the flour is incorporated into the oil and veggies.
Add canned coconut milk, soy sauce, brown sugar, lime zest, and lime juice. Allow the sauce to begin to thicken for 3-4 minutes.
Add the chicken to the sauce and heat until the chicken is cooked through.