Add remainder of dressing to a large resealable plastic bag with chicken thighs. Close bag and massage marinade into the chicken. Refrigerate for several hours if desired.
Heat a large skillet over MED-HIGH heat and drizzle a bit of olive oil into the skillet. Pat chicken thighs with a paper towel to remove excess marinade and cook chicken, about 4-5 minutes per side, until golden and cooked through.
Remove chicken to a plate to rest while you prepare the other ingredients.
Chop cucumber, onion, tomatoes, and olives and set aside.
To each bowl, add rice, some of the feta cheese, cucumbers, tomatoes, onions, and olives add a dollop of hummus or chickpeas and top with chicken.
Serve with whole grain pita or flatbread if desired.