Rinse the rice under cold water in a large bowl until the water runs clear, then soak at least 5 minutes.
Bring 3.5 cups water to a boil in a large saucepan, add the rice and 2 teaspoons salt, reduce heat to low, cover, and simmer about 10 minutes or until the water is absorbed and rice is tender.
Remove the pan from heat, stir in 2 tablespoons butter until melted, cover and set the rice aside.
Prepare the chicken marinade by whisking 3 tablespoons lemon juice, 3 tablespoons olive oil, 3 tablespoons chopped parsley, 3 crushed garlic cloves, 1 teaspoon paprika, and 1/2 teaspoon dried oregano in a large bowl or resealable bag.
Poke the chicken breasts several times with a fork, season with 1/2 teaspoon salt and 1/2 teaspoon pepper, add to the marinade, coat well, and marinate at least 20 minutes or up to 2 days in the refrigerator.
Remove chicken from the marinade and cook on a preheated grill, under the broiler, or in a grill pan over medium-high heat for about 5–6 minutes per side, until an instant-read thermometer registers 165°F (74°C) and juices run clear.
For the hummus, mince 2 cloves garlic in the food processor, then add 1 cup drained chickpeas, 1/4 cup tahini, 1/2 teaspoon kosher salt, the juice of 1 lemon (about 3 tablespoons), and 1 tablespoon water or reserved chickpea liquid; process until coarsely pureed and adjust consistency with more chickpea liquid if needed.
Make the salad by combining torn romaine, diced tomatoes, diced cucumber, halved kalamata olives, and thinly sliced red onion in a large bowl.
Whisk together 3 tablespoons extra-virgin olive oil, 2 tablespoons lemon juice, 1½ teaspoons oregano leaves (or 1/2 teaspoon dried), 1/4 teaspoon kosher salt, and pepper to taste, then toss with the salad and sprinkle with 1/4 cup crumbled feta.
Assemble bowls with rice, sliced grilled chicken, salad, and a dollop of chickpea-tahini hummus, then serve.