The best way, imho, to figure out the ideal chain length required is with a calculator such as
this. You might be lucky and don't need a new chain.
As you can see the small ring has no effect on chain length (but can affect whether the front and rear mechs are still ok, no problem in your case), it is the 3 extra teeth of the big ring that might call for a longer chain if the original is on the short side. You can also kind of check to see whether the chain still wraps around the pulleys nicely on the rear mech when you shorten the chain by pulling a couple of links together with your hand when the chain is on large front and back.