Combine chicken, lime juice, and 1 tbsp. curry powder in a large bowl, and toss to combine; refrigerate for at least 4 hours or up to overnight.
Heat oil in a 6-qt. Dutch oven over medium-high heat.
Season chicken with salt and pepper, and working in batches, add to the pot, and cook, stirring, until golden brown all over, about 8 minutes.
Transfer chicken to bowl with marinade, and set aside.
Add remaining curry powder, the allspice, garlic, scallions, thyme, carrots, chayote, potato, and ginger, and cook, stirring occasionally, until lightly caramelized, about 6 minutes.
Add chicken and any remaining marinade to the pot along with coconut milk and chile, and stir to combine.
Cook, stirring occasionally until chicken is cooked through and sauce is thickened, about 40 minutes
Serve over rice.