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Combine olive oil, 1/4 cup lemon juice, 2 cloves garlic, oregano and lemon zest. Pour half of marinade over chicken and marinate 15 minutes to 2 hours.
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While chicken is marinating, peel cucumber then cut in half lengthwise and remove seeds. Coarsely grate the cucumber using a box grater. Then wrap in paper towels and squeeze to remove excess liquid. You should have 1/2 to 3/4 cup grated cucumber
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Place cucumber in a bowl and stir in yogurt, remaining garlic, remaining lemon juice and dill.
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Remove chicken from marinade and thread onto 8 skewers.
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Grill chicken brushing with reserved marinade until browned on outside and no longer pink on the inside, about 8 minutes.
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Serve chicken on naan or flatbread and top with Tzatziki sauce and lettuce, tomato and red onion, if desired.