Slice onion in a food processor fitted with the slicing disk. Transfer to a bowl. Slice carrots using the same blade.
Heat oil in a 12-inch saucepan over medium heat. Cook chicken in the hot oil until no longer pink in the center, about 5 minutes. Add onion; cook and stir until soft, about 5 minutes. Add carrots; cook and stir until softened, about 5 minutes.
Stir dried cherries, cumin, coriander, garlic, and salt into the saucepan. Press down with a spatula to flatten chicken mixture into an even layer in the bottom of the saucepan.
Drain rice and place over chicken mixture in an even layer. Pour in 3 cups water. Cover and bring to a boil. Reduce heat to medium-low; simmer until water is absorbed and rice is tender, 10 to 12 minutes. Stir.