Combine the coconut milk, fish sauce, brown sugar, and curry powder in a large mixing bowl and stir well. Cut chicken thighs into generous, bite-sized chunks, and cut breast meat lengthwise into 1/2-inch strips. Add the meat to the marinade and mix well. Cover and refrigerate for at least 30 minutes or as long as overnight.

To prepare the peanut sauce, bring the coconut milk to a gentle boil in a medium saucepan over medium-high heat. Add the curry paste and roasted chili paste and cook 4 to 5 minutes, mashing and stirring occasionally to dissolve them. Add the chicken broth, fish sauce, palm sugar, peanut butter, and lime juice and cook 1 minute more, stirring well to make a smooth sauce. Remove from heat, transfer to a small serving bowl, and set aside to cool. The sauce can be served warm or at room temperature, or cover and refrigerate, reheating gently just before serving time.

Thread meat onto tips of bamboo skewers, and cook on a lightly oiled, hot grill or under a broiler, turning often, until browned and cooked through, 4 to 6 minutes. Serve at once with the peanut sauce and Tangy Cucumber Pickles.