For the buttermilk dressing: Whisk together the buttermilk, mayonnaise, chives, parsley, garlic, lemon zest and juice and 1 tablespoon water in a medium bowl. Season with salt and pepper and set aside.
For the grilled chicken and beans: Preheat a grill or grill pan (over 2 burners) to medium-high heat. Make a double thickness of aluminum foil about 18 inches square.
Toss the green beans with the olive oil and salt and pepper to taste and spread on one half of the foil. Fold the foil to seal the green beans in a rectangular package, leaving a little dome at the top. Put the green bean package on the grill and grill until tender, about 18 minutes. Remove from the grill and let the beans steam in the package until ready to serve.
Meanwhile, brush the onion rings with olive oil and season with salt and pepper. Grill on the other side of the grill until charred and tender, 8 to 10 minutes. Remove to a bowl when done.
Sprinkle the chicken with salt and pepper, brush with olive oil and squeeze the 2 lemon halves over. Grill the chicken, turning once, until cooked through, about 3 minutes per side. During the last 2 minutes, add the lemon quarters to the grill just to char.
To serve: Empty the green beans into the bowl with the onions and toss with 3 tablespoons of the dressing. Mound the vegetables on plates or a platter and top with the chicken. Drizzle with the remaining dressing and garnish with the grilled lemon wedges.
Cook's Notes: If cooking on an outdoor grill, the grilling can all be done at once, starting with the green beans, and then adding the onion after about 8 minutes and the chicken after 12. If cooking on a double-burner grill pan, grill the vegetables first and once they are done, grill the chicken all at once.
For an even quicker meal, you can purchase 8 chicken cutlets (about 2 pounds), instead of boneless skinless chicken breasts.