Project tracking open source Basecamp-like solutions

Once upon a time I've asked people on LinkedIn about collaboration software they prefer to manage their business and received a lot of interesting options that were optimal for different needs.

But I have my own specific needs, so decided to try only those that meets the following requirements:

• Open source - to be able to customise the system for our own needs
• Free of charge - I'm starting new low-investments business so can't afford to pay for subscription at this starting level
• Basecamp-like - at least more or less it should be similar to Basecamp from 37signals as they are gurus in usability as for me. I had an opportunity to work with dotProject but it doesn't satisfy my usability needs, because I was very impressed with Basecamp interface.
• PHP web development stack  - because I'm a PHP developer and want to be able to hack into the source code.