I cannot imagine why you would possibly want to know this, but the limit is quite large (dozens, probably hundreds deep) I'm sure. The limit is probably (but don't quote me) based on memory available, considering the number PPT entries possible and remembering that a LINK can go into another CICS region.
I want to know this because I was proposing a solution to an enhancemnet. we need to add 2 more link levels in the chain. Already six levels of LINK command are there. It would make them 8 after enhancement.i was wondering whether there is a limit..