Heat the oven to 350°F (175°C). Lightly grease a 9-by-13-inch baking dish so the chicken releases easily and the sauce is simple to spoon over at the table.

Place the four chicken breasts in the prepared baking dish in a single layer. If the breasts are unusually thick, pound them gently to an even thickness so they cook at the same rate.

Whisk the Russian dressing, apricot preserves, and dry onion soup mix in a bowl until the sauce is well combined. A few small pieces of onion mix are fine, but continue whisking until the preserves are distributed throughout.

Pour the sauce over the chicken, turning each breast so every surface is coated. Arrange the chicken in a single layer again, leaving the sauce pooled around and over the pieces.

Bake the dish uncovered for about 1 hour. Begin checking the thickest part of the chicken near the 50-minute mark, and continue cooking until an instant-read thermometer registers 165°F (74°C).

If the sauce starts browning too quickly, loosely cover the baking dish with foil for the remainder of cooking. Let the chicken rest briefly, then spoon the warm sauce over each breast before serving.