It really does depend on what you've got in the rest of your system. One of my machines is running an HD4650 on a 350W PSU with no problems at all, even though the manufacturer specs for that card say 400W. Manufacturer specs are generally going to err on the high side because they're just guessing at the setup for hte rest of your machine; you could theoretically have anything.
On the other hand, 300W is not a whole lot to work with. The 4670 doesn't use a whole lot of power, but like others have said, it's impossible to know without the rest of your system specs. I'd be surprised if it checks in at over 300W total, though.