Pound the chicken breasts to an even 3/4-inch thickness (this is the difference between juicy and dry — uneven chicken cooks unevenly).
In a large bowl or zip-top bag, whisk the olive oil, lemon juice, garlic, rosemary, thyme, 1/2 tsp of the salt, and the pepper. Add the chicken and turn to coat. Marinate 30 minutes at room temperature, or up to 4 hours in the fridge.
Heat a grill or grill pan over medium-high heat. Oil the grates (or pan) lightly.
Remove the chicken from the marinade, letting the excess drip off. Grill 6-7 minutes per side, until the thickest part hits 165°F on a meat thermometer (USDA safe temp — don't guess).
While the chicken rests, toss the asparagus with 1 tsp olive oil and the remaining 1/2 tsp salt. Grill 3-4 minutes, turning once, until charred in spots and tender-crisp.
Rest the chicken 5 minutes (the juices redistribute — skip this and they run all over the cutting board instead of staying in the meat). Slice against the grain and serve with asparagus and lemon wedges.