There are a number of important things to check when setting up a Rigid Body simulation :
Use the correct Collision Shape - on your example screenshot you show the first object as having Shape set to Mesh but check that all of your objects are similarly set. Convex Hull is more efficient but Mesh shape is required for interlocking objects and/or more complicated (non-convex) meshes.
Use a realistic scale - your example screenshot shows your Collision Sensitivity Margin set to 4cm which implies that 1 Blender Unit equates to 1 metre. Each link of your chain appears to be many blender units in size (when compared to the Grid which is visible in the screenshot). This means you have links that are many metres in length and will therefore behave as very large objects, with very large forces as they interact with each other. This can cause unstable simulations - especially if your 'steps per second' simulation setting is too low.
Ensure each object has its Scale applied - it's not clear if that is the case with your example. In order for Rigid Body objects to behave realistically, they need to have a consistent Scale in each of the X,Y,Z directions. To achieve this, select all links in the chain and press Ctrl+A and select 'Scale'.
Ensure the origin of each mesh is at its 'centre of gravity' - if you've created your chain using an Array modifier, split into its separate parts then the origins may be in the wrong place. Select the objects, click Set Origin in the tool panel (T) and select 'Origin to Centre of Mass'. A wrongly positioned origin (especially if it is outside the bounds of the mesh) can produce some very odd simulation results.
If the simulation still behaves erratically, you may need to increase the precision of the simulation - in particular the Scene/Rigid Body World/Steps Per Second - don't increase it too high as this can also cause problems with the simulation accuracy.
If you have addressed all of the above and still have a misbehaving simulation then it would help to upload an animation of what is occurring in your simulation (can tell a lot about how it's set up by how it moves and interacts) and/or upload your Blend file.
In order to demonstrate the difference applying the scale can make, here's a simulation where the chains have not had the scale applied (and have been stretched in one direction and have the scale of (1.0,1.0,5.0)) :
And here's the same simulation with the only difference being that the scale has been 'applied' (so they meshes are identical but scaled as (1.0,1.0,1.0)) :
