Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the chicken pieces to the skillet and cook until browned and fully cooked, about 5-7 minutes. Remove from skillet and set aside.
In the same skillet, add the sliced bell peppers, onion, and broccoli florets. Cook for 4-5 minutes, stirring occasionally, until the vegetables are tender-crisp.
Add the minced garlic to the skillet and cook for an additional 1 minute until fragrant.
In a small bowl, mix the sweet chili sauce, soy sauce, and lime juice. If you prefer a thicker sauce, mix in the cornstarch.
Return the cooked chicken to the skillet and pour the sauce mixture over the top. Stir to coat everything evenly.
Cook for another 2-3 minutes, allowing the sauce to heat through and thicken slightly.
Serve hot over cooked rice or noodles and enjoy!