Heat the vegetable oil in a large pot or Dutch oven over medium heat.
Add the diced onion, and sauté for about 5 minutes until softened.
Stir in the minced garlic and ginger, cooking for an additional 1-2 minutes until fragrant.
Add the diced carrots, celery, and apple to the pot, cooking for about 5 minutes until the vegetables start to soften.
Add the diced chicken to the pot and cook for 5-7 minutes, stirring occasionally, until the chicken is cooked through.
Sprinkle in the curry powder, ground cumin, turmeric, and cayenne pepper, stirring well to coat the chicken and vegetables with spices.
Pour in the chicken broth, and bring the mixture to a boil. Lower the heat and let simmer for 10 minutes.
Stir in the coconut milk and cooked rice, allowing the soup to warm through for an additional 5 minutes.
Season with salt and pepper to taste.
Serve hot, garnished with fresh cilantro and lemon wedges if desired.