Heat the vegetable oil in a large pot over medium heat. Add the chopped onion, garlic, and ginger, and sauté until the onion is translucent.

Stir in the curry powder and continue to cook for another minute.

Add the chicken breast pieces and cook until they are no longer pink.

Pour in the coconut milk and chicken broth, and bring to a simmer.

Reduce heat and let it cook for about 20 minutes until the chicken is tender and the sauce has thickened.

Stir in the lime juice, salt, and black pepper. Cook for an additional 5 minutes.

Serve hot, garnished with cilantro.