Heat 2 tablespoons olive oil in a large skillet over medium-high heat.
Salt & pepper chicken on each side, then sauté just until cooked, about 5-7 minutes on each side. (See notes)
Lower heat to low-medium and transfer chicken to a plate when cooked.
Add 1 tablespoon olive oil to skillet, then add red peppers and sauté until slightly softened, about 2-3 minutes, stirring throughout. Add the garlic and ginger, stir for another minute.
Slowly add coconut milk and lime juice. Stir, and bring to a low boil.
Return chicken to the pan and finish with most of the freshly chopped basil and cilantro (leave some for garnish!).
Cook time for the chicken depends on the size and thickness of your chicken. If your chicken breasts are very thick, consider slicing them in half in order to maintain the same stated cooking time; otherwise, plan for longer cooking time if your chicken breasts are thick.
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