Preheat grill to medium.
Heat 2 tablespoons oil in a large skillet over medium-high heat. Add cauliflower, onion and ¼ teaspoon salt. Cook, stirring occasionally, until the cauliflower is softened, about 5 minutes. Remove from heat and stir in ¼ cup dill.
Meanwhile, rub 1 teaspoon oil all over chicken. Sprinkle with ¼ teaspoon salt and ¼ teaspoon pepper. Grill, turning once, until an instant-read thermometer inserted into the thickest part of the breast reads 165 degrees F, about 15 minutes total. Slice crosswise.
Meanwhile, whisk the remaining 4 tablespoons oil, lemon juice, oregano and the remaining ¼ teaspoon each salt and pepper in a small bowl.
Divide the cauliflower rice between 4 bowls. Top with the chicken, tomatoes, cucumber, olives and feta. Sprinkle with remaining ¼ cup dill. Drizzle with the vinaigrette. Serve with lemon wedges, if desired.
