How can I replace the DLP chip in my projector?

Yes and no. Yes, but most DMD chips are significantly more than a used projector of the same group/model, or even nice used ones from companies like Epson who use the 3LCD system which doesn't break down like so many DLP models do where they tend to be a loss due to part cost. Dell also seems to have more issues then anyone else who uses DLP with how many of them have an issue like this but yours and the 1209s are infamously bad. The usual cause of this on problematic DLP models is bad cooling. Any DMD you put in is just as prone to death as the dead one you replaced.

The cost of the repair will likely be as much as a good model from a brand who doesn't have chronic problems but it can be done if you can find a good used DMD. Look for a different brand like BenQ or Optoma if you insist on DLP, otherwise give 3LCD a serious look. I have yet to see a 3LCD unit break due to a bad LCD assembly that isn't due to a fault that isn't the user or the unit being very old (10+ years) where once the lamp goes that's it because it's already discontinued anyway.