Preheat the grill to medium-high heat.
Season the chicken breasts with olive oil, garlic powder, paprika, salt, and pepper.
Toss the asparagus with a little olive oil, salt, and pepper.
Place the chicken on the grill. Cook for about 6–7 minutes per side, or until the internal temperature reaches 165°F (75°C).
Add the asparagus to the grill during the last 5–6 minutes. Turn them occasionally until tender and slightly charred.
Remove the chicken and asparagus from the grill.
Squeeze fresh lemon juice over everything.
Serve hot, garnished with fresh parsley if desired.