The first step is to create a torus that you will use for the chain link.

As you can see to the left I am creating a torus that has an overall diameter of 2 inches. In this example I am creating a torus with 16 segments and 12 sides.

Note:
You can use a lower resolution mesh and add turbosmooth when you are ready to render. By using an object with less faces you can get reatime viewport playback.

Now collapse the torus into a poly object. Then select half of the faces and detatch them to an element.

 

 

Once you have the two elements turn on Vertex snap and move one half of the mesh so that the two parts touch on the inside diameter (vertex to vertex).

 

Select the left half of the mesh and move it -1.5 in the x direction.

It is important you move the two parts a known distance since you will need to create a face that is the exact same distance.

 

Select the four open edges and use the Bridge tool to connect the two halves together.

Create a copy of the first chain link and move it -1.5 in the X direction. As you can see in the image the inner edge of the links should line up perfectly.

Select one of the links and go to its' subobject mode and rotate it 90 degrees.

By doing this you are not changing the pivot of the object which is important later.

Create a plane that is 1.5 units wide and 0.6 units long.

This creates a plane that lines up with the points where each link touches another. The 0.6 measurement is double the Radius 2 of the original torus. So the face matches the "thickness" of the link.

Move the plane from the midpoint of the shorter edge to the vertex at the middle of the inside edge as seen in the image to the left.

Create a copy of the plane and move it -1.5 units in the X direction.

Now select both links and both faces and use the spacing tool to space them 3.0 units apart. Make as many links as you need for the length of the chain.

 

In this image you can see the chain and the "Driver" mesh running though it.

Hide the chain links and select one of the faces in the "Driver"

Attach the other faces and go to Vertex subobject mode and weld all the verts together.

Make a duplicate of the mesh object and apply a meshsmooth to it. Be sure to UNCHECK the isloline display.

Collapse the meshsmoothed object.

From this point on the low poly mesh will be called the "Driver" mesh and the higher poly mesh will be called the cloth mesh.

Now Skin Wrap the "Driver" mesh to the "Cloth" mesh.

Use Face Deformation engine in the Skin Wrap modifier.

Now select all the chain links and run the Attach_Selection_to_Surface_by_Local_Z script (available from this site).

Once you run the script select the "Driver" mesh using the rubberband.

One last step is to rotate the links 45 degrees so that when the cloth object is flat on the surface of a collision object the chain will be lying on its' side (right) not on its' edge (left)

 

Create a cylinder to use as a collision object.

You are now ready to apply the ClothFX modifier. Select the "Cloth" mesh and the Cylinder and apply the ClothFX modifier.

This image shows the settings that I used for this demo.

As you can see I have the gravity set to -3000. I find that it helps to make the gravity stronger to make a cloth object look heavier. Typically, when I am doing clothing I start with -2000. In this case I want the chain to look much heavier so I have a higher gravity setting.

The Thickness of the cloth object should be the width of the chain link. This is only nessesary if the chain will be colliding with itself. If not you do not need to worry about the thickness of the cloth. The stretch settings are high and the "Use Edge Springs" checkbox is clicked so that the individual faces will not stretch (if they do then the links will come apart).

These are the settings for the collision object. The offset of the collision objects should be half the width of the chain link. This way when the chain is resting on the mesh it will not interpenetrate.

Once you run the simulation you will see the links pivoting and not bending.

The Red mesh is the cloth mesh
The green mesh is the "Driver" for the chain links
The Blue mesh is a cylinder collision object
The Grey mesh objects are the chain links

Here for a sample animation (mov) (wmv)