In a medium saucepan, whisk together the coconut milk, peanut butter, 2 tablespoons of the lime juice, brown sugar, 1 tablespoon of the curry paste, and the soy sauce. Bring to boiling over medium-high heat, then reduce to a simmer. Cook uncovered, whisking occasionally, until the sauce is thick enough to coat the back of a spoon, about 15 minutes.
Meanwhile, in a large bowl, whisk together the remaining 1 tablespoon lime juice, remaining 1/2 to 1 tablespoon curry paste, and oil. Remove the tenders from the chicken breast halves and set aside. Slice each chicken breast half lengthwise into 4 pieces. Add chicken strips and tenders to the bowl with curry mixture and toss to coat. Thread the chicken onto 10 10- to 12-inch wooden or metal skewers, 2 pieces per skewer (if using wooden skewers, soak in water for 30 minutes before using).
Preheat gas or charcoal grill to medium heat. Add skewers to grill rack. Grill for 15 minutes or until chicken is no longer pink inside, turning occasionally to brown evenly. Serve with sauce.