Oh man.. I totally forgot how to do this. The idea behind tension forces is that the Sum of all forces in the X direction must equal zero. The sum of all forces in the Y direction must equal zero.
Thus the Net-force of the system must equal 0. Using that, you solve the system for the force in each string/chain.
I obviously failed at doing so below but I did reduce the system a bit. That dotted line down the centre is the third string.

I don't remember if I'm approaching it right :l The diagram I drew kinda looks like the hanging weights problems.