In a large skillet combine chicken broth, lime juice, soy sauce, ginger, garlic and pepper. Bring to a boil and reduce heat to low and simmer. Add chicken and cook, covered for 8-10 minutes or chicken is no longer pink inside. Transfer chicken to a serving plate and cover with another plate or tinfoil to keep warm. Add brown sugar, peanut butter and sweet chili sauce to mixture and bring to a boil. Whisk mixture until blended. In a small cup combine coconut milk and cornstarch. Slowly add to mixture. Stir until thickens. Taste mixture and see if you need to add some salt or pepper or peanut butter. Add vegetables and chicken back into your skillet. Reduce heat and simmer for a few minutes or until vegetables are done to your liking. Serve with rice and enjoy!