I couldn't say without seeing your setup.
Is your derailleur short, medium, or long cage?
Single ring up front, or triple?
Largest sprocket on cassette 23 or 36?
Chain guide or none?
If it's a short cage, and you were running your chain fairly tight it may put undue stress on your derailleur.
If you run a chain guide you could always bypass it (take it off?) for a few days and get some extra length that way?
And when you say three links, do you mean three consecutive links ie: inner, outer, inner, or is it three complete links ie: three outer and three inner?
Got any spare powerlinks floating around?