Heat 2 tablespoons of oil in large skillet or wok over medium heat. Add the chicken and brown on all sides. Remove from pan and set aside.
Add sliced red pepper and onion to the pan and cook until softened (about 5 minutes).
Add the garlic and the chili peppers and cook about 30 seconds. Add the chicken back to the pan. Add the curry paste and brown sugar. Fry until fragrant.
Stir in the coconut milk. Stir the fish sauce, lime juice, and zest into the mixture; Add the herbs and lime leaves. Bring to a boil, lower to a simmer and cook until the sauce reduces and the chicken is cooked through (about 10 minutes).
Taste for saltiness and if more is needed, add more fish sauce if necessary and serve.
Use Fresh Garlic and Onion - The secret to making fantastic Thai curry is to use fresh aromatics, like onion and garlic.
Use full-fat coconut milk it adds a richness you don't get with the low-fat variety.
Kaffir lime leaves can be found dried in supermarkets or fresh in Asian markets, they also freeze well without losing flavor, so you can stock up.
You should be able to find Penang curry paste in your grocery store, but if you can't, it's well worth a trip to an Asian supermarket or buy it here on Amazon (#paidlink).