Make the marinade: Combine the onion, garlic, green chili, ginger, allspice, thyme, juice of 1/2 lime, and olive oil in a food processor. Pulse until smooth.
Marinate the chicken: Place the chicken in a large bowl, pour the marinade over it, and mix well. Cover and refrigerate for 5 minutes.
Cook the rice: Boil the rice in salted water until tender, about 15-18 minutes or follow package instructions. Drain and stir in the lime zest and cilantro.
Grill the kebabs: Thread the marinated chicken onto water-soaked skewers. Place under a broiler on high heat (230°C / 450°F) or over a grill on medium-high heat (200°C / 390°F) for 12-15 minutes. Turn every 2-3 minutes until the chicken reaches 74°C (165°F) internally.
Serve: Arrange the kebabs with the rice and lime wedges.