Heat 1 tablespoon of olive oil in a large pot or Dutch oven over medium heat. Add the chicken and season with salt and pepper to taste. Sauté until cooked through, about 5 minutes. Remove from pan and place on a plate, then cover loosely with foil.

Add the remaining 1 tablespoon olive oil to the pot. Add the onion and carrots and cook until softened, about 5 minutes. Add the garlic, ginger and turmeric, and sauté 30 seconds.

Add the bell pepper, pumpkin and green beans, and sauté 1 minute longer.

Add the the chicken back to the pan along with the red curry paste, coconut milk and water, and stir well to combine. Bring to a boil, then reduce the heat to medium low and simmer until the pumpkin is tender and the sauce has thickened, about 10-15 minutes.

Remove from heat and stir in the lime juice, cilantro and salt and pepper to taste.