Melt butter in a large oven-proof skillet over medium high heat. Add chicken, skin-side down, and sear both sides until golden brown, about 2-3 minutes per side; drain excess fat and set aside.
In a medium bowl, whisk together coconut milk and cornstarch; set aside.
Add garlic to the skillet, and cook, stirring frequently, until fragrant, about 1-2 minutes. Stir in ginger until fragrant, about 1 minute.
Whisk in curry paste until well combined, about 1 minute. Gradually whisk in coconut milk mixture, and cook, whisking constantly, until incorporated and slightly thickened, about 1-2 minutes. Stir in lime juice, fish sauce, sugar and sugar snap peas.
Return chicken to the skillet. Place into oven and roast until completely cooked through, reaching an internal temperature of 165 degrees F, about 25-30 minutes.
Serve immediately, garnished with chili pepper and cilantro, if desired.