Heat 1 tablespoon oil in a large skillet over medium-high heat. Add chicken, in batches if necessary, and cook, flipping once, until browned and cooked through, 1 to 3 minutes per side. Transfer to a plate.
Remove pan from heat. Whisk the remaining 1 tablespoon oil, coconut milk, brown sugar, curry paste and lime juice in the pan. Cook over high heat, stirring occasionally, until reduced by half, 5 to 10 minutes. Serve the chicken with quinoa and the sauce, garnished with cilantro, if desired.
