Heat oil in a medium saucepan over medium heat. Add onion and cook, stirring occasionally, until softened, about 3 minutes. Add curry paste and cook, stirring constantly, until fragrant, about 1 minute. Add rice and stir to coat. Add coconut milk and water; bring to a boil over high heat. Cover, reduce heat to low, and simmer until the rice is tender and the liquid is absorbed, 40 to 50 minutes.
Meanwhile, heat a grill pan over medium-high heat. Coat with cooking spray. Mix thyme, garlic powder, allspice, cayenne, cinnamon and ½ teaspoon salt in a medium bowl. Add chicken and toss to coat. Grill the chicken, turning once, until an instant-read thermometer inserted in the thickest part registers 165°F, about 12 minutes total. Transfer the chicken to a clean cutting board and let rest.
When the rice is done, stir in peas, cilantro, lime juice and the remaining ¼ teaspoon salt with a fork. Cover and let stand for 3 minutes.
Serve the chicken with the rice and more cilantro and lime wedges, if desired.