In a small bowl, whisk together the extra virgin olive oil, lemon juice, lemon zest, minced garlic, sea salt, black pepper, and dried oregano to create the marinade.
Place the chicken breast in a shallow dish and pour half of the marinade over it, turning to coat thoroughly.
Trim the woody ends off the asparagus and toss the spears with the remaining half of the marinade in a separate bowl.
Preheat a grill or grill pan over medium-high heat until hot.
Place the chicken on the grill and cook for approximately 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 slightly charred.
Remove everything from the heat and let the chicken rest for 5 minutes before slicing it into strips.
Plate the sliced chicken alongside the grilled asparagus and serve immediately.