Wrt the OP, I would say the answer is "it depends". I know people who do use the chromebook for programming, but they make use of cloud-based IDEs like Cloud 9. I haven't used it, or similar alternatives, so I can't comment too much on how viable they are as a development platform. The people I know who use it like it though; then again they mostly do web and mobile development.
That said, I suspect there are some pros and cons to such a system (such as the loss of overall control). If that's the case, some of the approaches described earlier in this thread might be possible or just buy a regular Windows / Linux laptop. For my part I don't use such systems for a variety of reasons, including the fact that they generally don't cover what I need (embedded DSP, etc). As a student, you will want to plan ahead a few years before you purchase your laptop. Figure out whether you actually will need any oddball or niche software in the years to come; you may not be able to install such on a chromebook.