In a small bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, dried oregano, sea salt, and black pepper.
Place the chicken breast in a shallow dish or reusable bag and pour half of the marinade over it, ensuring it is well coated. Let it marinate for at least 20 minutes.
While the chicken marinates, trim the woody ends off the asparagus and slice the zucchini into rounds.
Preheat your grill or grill pan to medium-high heat.
Place the chicken on the grill and cook for 6-7 minutes per side, or until the internal temperature reaches 165°F.
In the last 5 minutes of cooking, toss the asparagus and zucchini with the remaining marinade and place them on the grill.
Grill the vegetables until tender and slightly charred, about 2-3 minutes per side.
Remove everything from the grill and let the chicken rest for 5 minutes before serving with the grilled vegetables.