In a very large bowl stir together the yogurt, paprika, olive oil, and salt. Add the chicken pieces to the bowl and turn to coat with the yogurt mixture. Cover the bowl with plastic wrap and marinate in the refrigerator for 2 to 8 hours.
Preheat oven to 400 degree F. Line a 15x10x1-inch baking pan with parchment paper. Cut the potatoes in half, and lay them on the parchment paper, cut side down, leaving a little distance between each potato.
Place the chicken pieces on the potatoes. Roast for 45 to 60 minutes or until chicken is done (170°F. for breasts, 180 degree F. for thighs and drumsticks). Serve with a green salad. (Cover and chill 2 chicken breast halves for Smoky Chicken Tacos with Pear Cheddar Salad later in the week.) Makes 4 to 6 servings.