Cook penne with tablespoon salt to 1 minute short of package time. Reserve 1 cup pasta water; drain.
Meanwhile, rub chicken with allspice, thyme, paprika, garlic powder, cayenne, sugar, chicken salt, and pepper. Heat oil in large skillet; cook 5 to 7 minutes per side until browned and at least 165°F. Rest on board.
Cook peppers 5 to 6 minutes until crisp-tender. Whisk coconut milk, broth, and cornstarch; add and gently simmer 3 minutes.
Slice chicken; return with juices and penne. Toss 1 to 2 minutes until pasta tender, adding reserved water if sauce thick.
Add lime juice off heat; serve with peppers and chicken evenly distributed.