Place 1/4 cup drained tomatoes in small bowl; set aside. Combine remaining drained tomatoes, chicken and cheese in medium bowl. Shape mixture into 4 rectangle-shaped patties (5x3 inches), about 1/2-inch thick.
Heat oil in large nonstick skillet over medium-high heat. Cook patties 5 to 6 minutes per side or until no longer pink in centers (165°F). Meanwhile, add mayonnaise to reserved tomatoes; stir together.
Cut bread into 4 pieces, about 5 inches each. Cut each piece in half lengthwise. Spread tomato-mayonnaise mixture on cut sides of bread. Place 1 lettuce leaf on bottom half of each piece; top with chicken patty. Cover chicken with top halves of bread. Serve immediately.
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