It may be easier to just install a flow valve on the cold water line under the sink with a standard hose adapter on one end and run a short piece of garden hose from that to your chiller. That way you don't have to take your faucet apart every time you brew.
Hm, interesting, didn't even think about that, that definitely sounds like a better way to do it. What exactly should I be looking for? I've never done anything like this before. Also, I'm just a renter—anything I should be worried about if I muck around down there that might break something?