What is the name of the river the children must cross in The Silver Chair?

The river the children must cross in The Silver Chair is the River Shribble.

Jill Pole, Eustace Scrubb and the Marsh-wiggle Puddleglum cross the Shribble while traveling north from Narnia toward Ettinsmoor, the wild land of the giants. The crossing takes place early in their quest to find the lost Prince Rilian and the ruined city connected with his disappearance.

Puddleglum initially presents the river as a serious obstacle, noting that there are no bridges and that it separates Narnia from Ettinsmoor. In practice, the Shribble is shallow: the travelers make their way across by shoals and stepping-stones, and Jill is not wet above her knees. The scene highlights Puddleglum’s famously gloomy habit of making dangers sound worse than they are.

The Shribble is not the Great River of Narnia, which flows across Narnia toward the Eastern Ocean. Nor should it be confused with the Sunless Sea or Silver Sea, both associated with other parts of Narnian geography.