Preheat a grill or grill pan over medium-high.
In a small bowl, mix the spices with 1 tsp. salt and 1/2 tsp. pepper. Season the chicken on both sides with the spice mixture. Grill, skin side up, 5 minutes, then turn and grill until the skin is crispy and the chicken is cooked through, about 5 minutes more. Transfer to a plate.
Meanwhile, in a large bowl, toss the pineapple and onion with the oil; season. Grill, turning occasionally, until charred in spots, 8 to 10 minutes. Transfer to a cutting board; chop into small pieces. In the same large bowl, toss the chopped pineapple and onion with the cilantro and lime juice; season. Serve the pineapple relish with the chicken.