Pat the chicken slices dry with paper towels to help them brown well.
Heat the vegetable oil in a large skillet or wok over medium-high heat until hot but not smoking.
Add the minced lemongrass, garlic, and optional chili to the pan. Stir-fry for about 30 seconds until fragrant, taking care not to burn the garlic.
Add the chicken to the pan in a single layer. Allow it to cook without stirring for 2 minutes to develop a slight caramelization.
Stir-fry the chicken, tossing and turning gently, until it is cooked through and lightly browned, about 5–6 minutes total.
In a small bowl, mix the fish sauce, soy sauce, and brown sugar until the sugar dissolves.
Pour the sauce over the chicken and stir to coat evenly. Cook for an additional minute until the sauce slightly thickens.
Remove from heat, garnish with chopped cilantro and green onions.
Serve immediately with steamed rice or your favorite side.