It's a bit messy, as my original solution didn't work on the live server and I had to rethink it. My second plan was to reduce it to a handful of potential chunks I could brute force. Once I got it running, though, I realized it was eliminating about half of the chunks on each pass, which left me with the correct one in 7-13 iterations.
I actually had no problems with chunks 1 and 2. Half way through chunk three the server started acting up so I aborted my script and added the modifications that I mentioned above. I tweaked the server and client so that they had a hard coded value for chunks 1 and 2.
https://gist.github.com/38c0430b5084f8442858 for my entire implementation.
Edit: saw the answers above - it's 2400 average case, not worst case.
Chunks of the password (of equal size, see the code) were stored in multiple chunk servers. From crashing the program or reading the code, it could be determined there were four chunk servers, so each hosted three characters of the password.
Using a port-counting vulnerability (sending multiple identical requests, and rejecting guesses where the difference in response port #s was too low: 2 for first chunk, 3 for second chunk, etc.) it was possible to brute force each chunk server in sequence.
Thus, the problem space was 4*10^3 rather than 10^12.
You only need 1 call per possible number for each chunk, yes. But since the numbers are random between 0 to 999, that averages to 500 requests per chunk. Additionally, you don't have to do any kind of port checking for the last chunk, so that saves on any overhead you might have for the port checks. Based on this I'd say there's (3x 500 requests + 20% overhead) + 500 requests for the final block. That's 2300 requests on average.