In a bowl, combine olive oil, lemon juice, minced garlic, oregano, salt, and pepper to create the marinade.
Place chicken breasts in the marinade, cover, and refrigerate for at least 30 minutes.
Preheat grill to medium-high heat.
Remove chicken from marinade and grill for 6-7 minutes per side, or until internal temperature reaches 165°F.
While chicken grills, place broccoli, carrots, and snap peas in a steamer basket over boiling water.
Cover and steam vegetables for 5-7 minutes until tender but crisp.
Serve grilled chicken with the steamed vegetables on the side.