Combine oil, lemon juice, oregano, and garlic in a food storage bag.
2
Butterfly each breast and add to food storage bag. Marinate in refrigerator for one to two hours. Turn bag occasionally.
3
Peel cucumber. Grate cucumber into a colander or mesh bowl. Sprinkle with sea salt n]and set inside larger bowl to catch liquid. Refrigerate for 15 minutes.
4
After 15 minutes, squeeze remaining liquid from cucumber. Mix in dill and garlic. Refrigerate for several hours so flavors can blend. Season with additional salt and pepper, if desired. When ready to serve, add 1/4 cup of pistachios and mix.
5
Preheat grill to medium hot. Remove chicken from marinade. Sprinkle with salt and pepper. Grill 2 to 3 minutes per side or until cooked through.
6
Place each breast on a serving plate, top with yogurt sauce, and sprinkle remaining pistachios on top.