10-speed blocks and chains...

Less facetious answers:

• chains aren't "brand" specific: it's just the number of gears that's relevant.
  
• shifters and rear derailleur (front are less fussy) need to match, as does the cassette (unless 11 speed).
  
  

Reading between the lines (and more carefully), it sounds like you want to run a 10 speed Shimano wheel/cassette with Campag shifters: that won't work.

Shimano/SRAM cassettes are spaced differently between the sprockets compared to Campag, so the indexing will be out.

Shimano/SRAM freehubs have a different spline pattern compared to Campag, so you can't just swap cassettes either.

Having said that, there are some combinations that do work: from memory I think 10 speed Campag shifters work with 9 speed Shimano cassettes: search for "shimergo", there's a thread on here and the CTC forum is a good reference.