In a medium-size heavy-bottomed saucepan, heat the coconut and olive oils over medium heat. Add the garlic and cook until fragrant, about 1 minute, being careful not to burn.
Add the chicken and sauté until slightly browned, about 1 minute. Add the cilantro, parsley and salt and stir together well. Add the water and cover with a tight-fitting lid.
Cook until the chicken is fully done, and the sauce has reduced to a thick paste, about 30 minutes. Make sure the bottom does not burn, by stirring occasionally and lowering the heat if necessary.