Add 2 tablespoons oil to a large skillet set over medium heat. Once the oil is hot, add the onions, garlic and red peppers. Cook, stirring constantly, until the onions are translucent, about 3 minutes. Add the curry paste and curry powder and cook, stirring constantly, an additional 2 minutes.
Push the vegetables to one side of the pan then increase the heat to medium-high.
Add the remaining 1 tablespoon oil then add the chicken and a pinch of salt and cook, stirring occasionally, until it is browned on all sides, about 5 minutes. (It does not have to be fully cooked at this point.)
Stir in the coconut milk and peas then bring the curry to a simmer and cook, stirring occasionally, until the chicken is cooked through and the sauce has thickened slightly, about 5 minutes.
Remove the curry from the heat then stir in the lime juice. Taste and season with salt then serve over rice.