Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the minced lemongrass and garlic, sautéing for about 1 minute until fragrant.
Increase the heat to high and add the sliced chicken. Stir-fry for 5-7 minutes until the chicken is cooked through and no longer pink.
Add the sliced red bell pepper and snap peas to the skillet. Stir-fry for an additional 3-4 minutes until the vegetables are tender-crisp.
In a small bowl, mix together the soy sauce, fish sauce, brown sugar, and black pepper. Pour this sauce over the chicken and vegetables, stirring to coat everything evenly. Cook for another 2 minutes.
Remove from heat and stir in the chopped green onions.
Serve the lemongrass chicken stir-fry over cooked jasmine rice.