In a large skillet, heat the vegetable oil over medium-high heat. Add the chicken pieces and cook until browned and cooked through, about 5-7 minutes.
Pour the teriyaki sauce over the cooked chicken and stir to coat evenly. Let it simmer for 2-3 minutes until the sauce thickens slightly.
While the chicken is cooking, steam the broccoli, carrots, and snap peas until tender, about 4-5 minutes.
To assemble the bowls, divide the cooked rice among four bowls. Top each bowl with the teriyaki chicken and the steamed vegetables.
Garnish with sliced green onions and sesame seeds, if desired. Serve immediately.