At the moment, adding labels to edges that branch or join chains in TikZ seems to be unsupported. See, for instance the discussion (and links) here: http://tex.stackexchange.com/q/40848/15911
The available workarounds are cumbersome and unreliable.
Please add to TikZ support for labelling any edge in any chain.
The chains library is now outdated. The graphs library and its friends are more powerful and easier to use. There, adding a label to edges is very easy. I do not indent to work on the chains library any more.