In a small bowl, whisk together 2 tablespoons of olive oil, lemon juice, minced garlic, oregano, salt, and pepper.
Place chicken breasts in a resealable bag and pour half of the marinade over them; marinate for at least 30 minutes in the refrigerator.
Preheat an outdoor grill or grill pan to medium-high heat (approximately 400 degrees Fahrenheit).
Toss the trimmed asparagus with the remaining 1 tablespoon of olive oil and a pinch of salt.
Place chicken on the grill and cook for 6 to 7 minutes per side, or until the internal temperature reaches 165 degrees Fahrenheit.
Add the asparagus to the grill during the last 5 minutes of chicken cook time, turning occasionally until tender-crisp and lightly charred.
Remove from heat and let the chicken rest for 5 minutes before serving alongside the grilled asparagus.