Vegetable oil, for the grill
Four 6- to 8-ounce boneless, skinless chicken breasts
Kosher salt and freshly ground black pepper
Zest and juice of 1/2 lemon
2 ripe peaches, pitted and cut into wedges
2 large tomatoes, preferably heirloom, cored and cut into wedges
1/4 cup lightly packed basil leaves, torn
2 tablespoons roughly chopped chives
1 tablespoon extra-virgin olive oil, plus extra for drizzling