Cut up chicken into cubes and place in a large resealable plastic bag. Mix all marinade ingredients in a small bowl. Pour marinade over the chicken, seal, and refrigerate for at least 1 hour. Skewer chicken (remember to soak your skewers if they are wooden) and place on grill over medium-high heat, turning 1/4 turn every couple minutes. When chicken is cooked through and juices run clear, remove from heat.
Crock Pot Method
Add butter and onions to crock pot. Stir onions around to coat in butter.
Add chicken to the bottom of the crock pot, placing the pieces evenly over the onions. Add lemon zest, lemon juice, chicken broth, oregano, and salt and pepper. Cover and cook on high for approximately 2 hours or on low for 3-4 hours.
Assembling the Gyros
While the chicken is cooking in either method, combine all tzatziki ingredients in a bowl and mix together. If you want a more smooth sauce, you can blend the sauce in a food processor. Store in the fridge until ready to eat.
Once the chicken is done, assemble the gyros by placing a flatbread down and topping with chicken, tzatziki sauce, and any other toppings you prefer.
Nutrition Information is for crock pot method and does not include toppings other than tzatziki sauce.