Turn heat to low and add in curry paste. Stir until fragrant, about 1-2 minutes. Add in chicken broth and coconut milk, stir until well combined and then add chicken. Turn heat up to high until the broth is boiling then turn it down to simmer for at least one hour and preferably 1.5 hours.
Transfer the chicken to a cutting board. Using two forks, separate the meat from each piece of chicken, placing only the meat back into your pot.
Top with fresh cilantro and serve over white rice!