Using a new chain on worn out sprocket? I went to REI yesterday because my bottom bracket was creaking.  I brought my bike with me so I could get the right tools to take it off, but while I was there the mechanic actually took the crankshaft apart, cleaned, and lubed everything for me (I guess it was a slow day).  He also checked my chain with a little gauge and said that it's more than 100% worn.  He said that it is so worn out that my back set of sprockets could be damaged from it.

The mechanic said that I should replace my chain every 2000 miles.  I have been using my current one for about 3000.  Is 2000 miles a good distance to replace a chain?  (I've never had this problem on my mountain bike.  I always replace the chain every summer because of rusting.  I didn't even know that it could actually wear itself out.)

I went home and ordered this chain on eBay.  If I put it on my bike and my sprockets are indeed worn out will it wear out my new chain quickly?  How will I know if I should replace the back COG?

Thank you.

PS: The chain I ordered has a Titanium coating, does that mean it will last longer than a "normal" chain, or is it just advertising?  KMC says it can last "up to" 10k miles, is that true?  Does anyone have any opinions of KMC chains?

Also, this is my first road bike, and I don't know too much about them.  I got it for my birthday for commuting to school (and work in the summer).
If your chain was measured and is worn, then by all means replace it.  You are going to cause more wear to your bike using a worn chain than having slightly worn sprockets.  A worn chain causes uneven wear on the teeth of your chainrings and cassette cogs, eventually this can cause issues with shifting and 'chain suck'.

The new chain you selected looks good. Before you install it, please clean off any grease and grime from your front chainrings and cassettes.  It should be good without re-lubing for a couple hundred miles with the factory lube, after that you should make sure that you keep it clean and lubed regularly.  

The life of your chain is proportional to how you maintain it, a good chain poorly maintained will last a couple thousand, well maintained I don't doubt it could last 10k.

More info on chains: http://sheldonbrown.com/chains.html