I had the same faucet, too.
I used an ice bath at first. Then, I had a utility sink installed in my basement, and now I run a tube from my kitchen down to my basement, where I hook up a plate chiller.
I had considered a couple of workarounds:
1.) Splitting off the cold water under the sink with a wye connector and a stopcock.
Pros: stays out of the way.
have to fiddle around under your sink.
You introduce the possibility of leaks
under your sink.
2.) A giant funnel using gravity to push the cooling water through the chiller. If you're brewing in your kitchen, you could use the loop at the top to hang the funnel from the top of the cabinet above your sink. Better yet, you can use a utility knife to cut a notch out of the side of this funnel, then stretch the faucet up and hang it so that it empties into the funnel. I'm not up to speed on fluid dynamics, but I think you could get enough pressure out of the gravity feed.
Pros: Cheap. Stowable.
Cons: Potentially messy. Ugly while not stowed. Untested.