PvZ, Lings deny natural? (Silver league)

How do I deal with this? I try to expand, then 20 lings show up while I have something like 3 zealots and 4 stalkers. They kill expansion, and leave, and I get so far behind in econ that I basically have lost already at that point. I realize I made a bunch of mistakes afterwards, this has happened several times in a row so when it happened again I was put on some serious tilt.

Replay