Rinse and drain farro. Place farro in a pot with salt and enough water or stock to cover it. Bring it to a boil; reduce heat to medium-low and simmer for 30 minutes. Drain off any excess water.
For the chicken: In a gallon size zip bag, combine chicken breasts, olive oil, lemon zest, lemon juice, garlic, oregano, salt, and pepper. Marinate for 4 hours or overnight.
In a large skillet, heat olive oil over medium-high heat, add the chicken breasts into the skillet and cook for 7 minutes, flip, and continue to cook for another 5-7 minutes until the internal temperature has reached 165. Discard marinade.
Remove chicken from pan and wait 5 minutes before slicing.
To assemble the Greek bowls, place a bed of farro at the bottom of your bowl or meal prep container. Top with sliced chicken, tomatoes, cucumber, olives, red onion, tzatziki sauce, and feta cheese. Sprinkle some parsley and dill, cover with the lid.
Divide Tzatziki into lidded sauce containers and pack with the chicken bowls.