Blend first 3 ingredients in bowl; season mayonnaise with salt and pepper.
Using meat mallet, flatten chicken breast halves in plastic bag to 1/2-inch thickness; cut chicken crosswise in half. Place on sheet of foil. Brush chicken with 1 tablespoon oil; sprinkle with half of garlic, then salt and pepper.
Place zucchini and onion slices on sheet of foil and brush with remaining 2 tablespoons oil; sprinkle with remaining garlic, then salt and pepper.
Prepare barbecue (medium-high heat). Grill chicken pieces until cooked through, about 5 minutes per side; transfer to work surface. Grill vegetables until softened slightly and charred, about 7 minutes per side for onion and 5 minutes per side for zucchini. Transfer to work surface.
Grill rolls until toasted, about 2 minutes per side. Spread tarragon mayonnaise on roll bottoms; top with 1 chicken piece, 1/4 of grilled vegetables, and 2 tomato slices. Cover with roll tops.