4 lemongrass stalks, tough outer layers removed, chopped
1 medium shallot, chopped
2 garlic cloves, chopped
1/4 cup fresh lime juice
2 teaspoons fish sauce
2 teaspoons light brown sugar
1/2 teaspoon crushed red pepper flakes
4 6-ounce skinless, boneless chicken breasts, pounded to 1/2-inch thickness
Kosher salt, freshly ground pepper
2 tablespoons vegetable oil
Lime wedges (for serving)
Process lemongrass, shallot, garlic, lime juice, fish sauce, brown sugar, and red pepper flakes in a food processor to a fine paste. Season chicken with salt and pepper and place in a resealable plastic bag. Add lemongrass mixture; chill at least 30 minutes.
Heat oil in a large skillet over medium-high. Remove chicken from marinade, scraping off excess, and cook until golden brown, 6–8 minutes; turn and cook until cooked through, about 2 minutes longer.
Serve chicken with lime wedges for squeezing over.
Do Ahead: Chicken can be marinated 2 days ahead. Keep chilled.