In Minecraft on the Xbox One, the drops from the hoppers are not going into the nearby chest. How do you connect them?
The chest cannot just be "nearby" the hopper output must be right on the chest.
From the wiki:
To place a hopper, use the Place Block control while aiming at the surface to which its output should face (a hopper will not automatically orient itself to point at a container). To place a hopper so that it faces a container (or other block which has a Use Item interaction), sneak while placing the hopper. A hopper placed while aiming at the bottom of a block will re-orient to face down instead. Hoppers won't change their direction after being placed and aren't "attached" to the container they are facing -- the container can be removed and the hopper will continue to face in the same direction.