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Place thighs in a large zipper-lock bag. In a medium bowl, whisk together soy sauce, fish sauce, sugar, ginger, chili-garlic paste, lime juice, lime zest, garlic, cilantro, and oil. Pour marinade into bag with chicken, seal bag, and toss to coat well. Let chicken marinate for at least 30 minutes and up to 4 hours.
Preheat oven to 425°F (218°C) and set oven rack to middle position. Line a rimmed baking sheet with foil and place a wire rack on top. Remove chicken from bag, allowing marinade to drip off, and set on wire rack skin side up, making sure to leave space between thighs. Discard marinade. Bake until thighs register 155 to 160°F (68 to 71°C) on an instant-read thermometer, about 35 minutes. (Be sure to measure temperature in the center of the thickest part of the thighs, but not directly against the bone.) If chicken skin is not brown and crisp enough by the time the thighs are cooked through, turn on oven broiler and broil until browned and crisp, about 1 minute, being careful not to burn the skin. Transfer chicken to a platter and let rest for 5 minutes. Garnish with lime slices and cilantro, then serve.