Smash the garlic clove, sprinkle with 1 teaspoon of salt and with the flat side of a large knife, mash and smear to a coarse paste. Put the garlic paste in a large bowl and stir in the olive oil and lemon juice. Add the tomatoes, cucumber, pepperoncini, and dill and toss. Give a couple of generous grinds of black pepper. Toss again, and set aside.
Preheat a grill pan or nonstick skillet to medium high. Spray the chicken paillards lightly with the olive oil and season with salt and black pepper. Grill the chicken, in batches if necessary, to avoid crowding the pan, turning once, until cooked through, about 2 minutes per side. Place each paillard on a plate and serve topped with the tomato-cucumber salad.
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