Place a large deep skillet over medium heat and add the oil. Season the chicken breasts with salt and pepper. Once the skillet is hot add the chicken breasts and cook 4 minutes per side.
Meanwhile, peel the onion and garlic cloves. Place the parsley, onion, garlic, vinegar, oregano, cumin, crushed red pepper, and 1/2 teaspoon salt in the food processor. Pulse until the mixture is well chopped. Then add in the cream cheese and water. Turn on and puree until very smooth.
Once the chicken has seared 4 minutes per side, pour the sauce over the chicken. Simmer for 3-5 minutes to let the chicken finish cooking and the sauce thicken. Taste, then salt and pepper as needed.
Don't have a food processor? The sauce can be made in a high power blender. Blend all the ingredients at once.