The relationship between the crow and the rat is predator-prey.
In a predator-prey relationship, one organism (the predator) hunts, kills, and eats another organism (the prey) for food. In this scenario, the crow is the predator, and the rat is the prey. The crow chased away the rat and ate its food, which means that it hunted and killed the rat's potential food source. Therefore, the relationship between the crow and the rat is predator-prey.