Place chicken in a gallon-sized resealable plastic bag. Whisk together fish sauce, lime juice, sherry, brown sugar, chili sauce, minced garlic, Sriracha sauce, sesame oil, and lemongrass paste in a bowl and pour over chicken. Seal the bag and toss to coat. Refrigerate for at least 2 hours, but up to 8 hours for maximum flavor.
Preheat an outdoor grill to medium-high heat and lightly oil the grill. Remove chicken from marinade, discarding marinade.
Grill until chicken is no longer pink in the center and the juices run clear, about 12 minutes total, turning halfway through the cooking time. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Transfer to a serving platter and let rest 5 minutes.