In a large microwave safe pot with a lid, mix together curry paste, oil, and peanut butter. Cover and microwave on high for 2 minutes. Add chicken to the pot and stir. Cover with the lid and microwave on medium for 8 minutes.
Add basil, cilantro, coconut milk, soy sauce, and brown sugar and season with salt and pepper. Stir to mix very well, cover it, and microwave on medium for 4 minutes. Stir again, cover, and let it rest for 3 to 4 minutes.