Cut the chicken breasts into 1 inch cubes. Place in a shallow bowl with the lemon zest and juice, oregano, garlic cloves, olive oil, and 1 teaspoon salt. Refrigerate for at least 2 hours minutes, or up to 12 hours, stirring occasionally.

Place the skewers in a shallow pan of cold water and allow to soak for at least 30 minutes. This will protect them from scorching on the grill.

Preheat a grill or grill pan over medium heat. Thread the chicken onto skewers.

Place on the grill and let cook for 2–3 minutes or until grill marks appear. Flip and continue cooking, turning occasionally, until the chicken is no longer pink in the center, about 10–12 minutes total.

About 10 minutes before you begin grilling the chicken, place 4 cups of water, rice, turmeric, and 1 teaspoon of salt in a medium saucepan over high heat. Bring to a boil, then reduce the heat to low.

Cover and cook until the water is absorbed, typically about 20 minutes though it depends on the style of rice (check the package for exact directions). Remove the lid, fluff with a fork, and set aside.

Grate the cucumber using a box grater. Place the cucumber in a fine mesh sieve or strainer and place over a bowl. Use the back of a spoon or spatula to press the water out of the cucumber. Keep pressing until no more water is released from the cucumber.

Place the grated cucumber, Greek yogurt, garlic, lemon juice, olive oil, and salt in a small bowl. Stir to combine. Refrigerate until ready to serve.