This is a weird strategy. When you feel the guy is going for many zerglings before teching to either hydralisks or mutalisks, you have the right strategy in your hands to kill him. First off, start with the usual 8 probes then pylon.

Make your first gateway as soon as you have the money (around 10/17) and never stop pumping zealots from it. Before your 1st gateway finishes, build an assimilator. Then, make another pylon, and warp a forge (you should already be getting gas with three probes at this moment).

As soon as your forge is warped, research the attack upgrade. Don't forget to warp zealots meanwhile. You should be at around 20/25 with two zealots up the ramp.

As soon as you have the crystals needed, warp another gateway and start massing up zealots while the upgrade is getting researched. Add pylons whenever needed. By the way, it is normal to have a huge amount of gas not used yet. Later, when you'll really need it (for templars and fast legs zealots), it is going to be useful. You should have around 34/41 of population, with 4-6 zealots ready to attak and other being warped.

As soon as your attack upgrade is completed, rush toward zerg expand. At this point, you should have around 10 zealots 1-0-0 ready to BURN zerglings. The unexplained trick here is the fact that 1-0-0 zealots kill a zergling in 2 hits instead of 3 when they are upgraded. Meanwhile (or just a little bit before your attack upgrade is completed, start teching to templars).

See how MAD those zealots seem to be :) . They are going for a mad rape. Remember to micro them when you attack; don't send them in a long line. Make a big pack and send them all at once so they all attack zerglings or hydralisk at the same time. Also, whenever possible, back off a little bit an almost dead zealot and make it attack again right after. You can save many zealots that way. My BW name is {KS}Shadow play me if you want to a very skilled opponent! This strat only works if your opponent is going mass lings! If your attack dosn't work it is imparative that you have some sort of defence, and more stuff, standing bye! Then just start teching up and try something else :-)

CreepColony's Opinion: I think by the time you upgraded 1 level of ground weapons, your opponent won't be building zerglings anymore.