Brush each of the chicken breasts with the olive oil, then season both sides with the salt and pepper. Grill over hot coals, turning once, until golden brown and thoroughly cooked; cool, then cut into 1/2-inch chunks.
Combine cooled chicken with the Roasted Garlic mayonnaise, celery and green onions.
To serve, arrange one-fourth of the salad greens on each of 4 plates. Arrange pepper slices on top of greens, then drizzle some of the vinegar and olive oil over each portion, along with additional seasonings of salt and pepper.
Finally, spoon on chicken salad mixture. Serve immediately.
Roasted Garlic Mayonnaise: Roast 8 garlic cloves, still in their skins, in 1 tablespoon olive oil in an oven-proof dish at 350 F until soft when pressed, about 45 minutes to 1 hour. Let garlic cool, peel away outer skins and place garlic pulp and oil from roasting dish in bowl of a food processor, along with mayonnaise, fresh lemon juice and Dijon-style mustard. Process until garlic is pureed and mixture is smooth. Season with salt and pepper, to taste. Makes about 1 3/4 cups.