There are several issues with your file:
The object origins are not centered. The origins are used to calculate the center of mass, which means that they can result in strange behavior if they are not correctly centered. Press CtrlShiftAltC> Origin to center of mass to snap the origin to the center of mass.
The intersecting concave links are using the Convex Hull collision shape. Because the hole in the middle of each link is a concave shape, the links then collide and fly apart. To the simulator it appears as if the links are inside one another.
However, note for a chain I recommend using Constraints instead.
Some objects have unapplied transforms. In many cases applying the scale and rotation can improve the stability and behavior of a simulation. Just beware when applying transforms to animated objects.
Animated is not enabled on the capstan. Enabling this is important if you want to control rigid bodies with the animation system.
Setting up Constraints for a chain:
Select all the links in the chain.
Press Connect in 3D View > Tool Shelf > Physics > Rigid body tools, then set the constraint type to Point (sort of a ball joint) and the Connection Pattern to Chain by distance:
By default the new constraints (added to the empties) will have Disable collisions enabled which disables collisions between objects constrained to each other. I recommend leaving this setting on, and keeping the collision shape on Convex Hull as nothing besides the links themselves are likely to try and pass through the hole.
(For Blender 2.8)