Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the chicken pieces and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced lemongrass, garlic, and ginger. Stir-fry for about 1-2 minutes until fragrant.
Add the sliced red bell pepper and snap peas to the skillet. Stir-fry for another 3-4 minutes until the vegetables are tender-crisp.
Return the cooked chicken to the skillet. Add the soy sauce, fish sauce, brown sugar, and lime juice. Stir well to combine and cook for an additional 2 minutes, allowing the flavors to meld.
Serve the stir-fry over cooked jasmine rice and garnish with fresh cilantro.