For the gremolata: Smash the garlic cloves, sprinkle with the salt, and with the side of a large knife, mash and smear the mixture to a coarse paste. Chop the parsley leaves with the garlic paste. Stir the parsley mixture with the lemon zest, juice, and olive oil in a small bowl. 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, to taste. Grill the chicken, in batches if necessary, to avoid crowding the pan, turning once, until cooked through, about 2 minutes per side. Put each paillard on a plate and top with the gremolata.
Toss the arugula, radicchio, and tomatoes with the 1 teaspoon olive oil, lemon juice, salt and pepper and divide among the plates. Serve immediately.
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