Slice chicken into thin strips and season with salt and pepper.
Heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add the chicken slices and cook until just cooked through (see notes).
Once the chicken is cooked, lower heat to medium and transfer chicken to a plate. Set aside.
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 stir in with the sauce. Add most of the freshly chopped basil and cilantro (leave some for garnish), and stir together, cooking just until the basil and cilantro leaves have softened.
Notes
Makes approximately 4 servings.Storage: allow the chicken to cool, then store in an airtight container in the refrigerator for up to 4 or 5 days.Chicken doneness: Cook time for the chicken depends on the size and thickness of your chicken slices. Try to cut evenly sized slices so the chicken cooks up evenly. Chicken is done when a meat thermometer shows an internal temperature of 165°F.