In a small bowl, whisk together the extra virgin olive oil, lemon juice, lemon zest, minced garlic, dried oregano, sea salt, and black pepper.
Place the chicken breast in a shallow dish and pour half of the marinade over it, ensuring it is well coated; let it marinate for at least 15 minutes.
Trim the woody ends off the asparagus and toss the spears with the remaining half of the marinade in a separate bowl.
Preheat your grill or grill pan to medium-high heat.
Place the chicken on the grill and cook for 6 to 7 minutes per side, or until the internal temperature reaches 165°F.
During the last 5 minutes of the chicken's cooking time, add the asparagus to the grill and cook, turning occasionally, until tender and lightly charred.
Remove everything from the grill and let the chicken rest for 5 minutes before serving alongside the asparagus.