Make sure the person asking for 300 DPI really knows he really needs 300 DPI, and actually ask about the LPI (Lines Per Inch) or better yet PPI (Pixels Per Inch) to be totally sure.
Just because your printer can print 300 DPI (DOTS per inch) does N O T mean you need a 300 PPI (PIXELS per inch) image.
Why? Coz a dot isn't a pixel. No, a *set* of dots build a pixel, because in a printer, a DOT can be either on or off, not inbetween. (Well, this sort of changes with some newer inkjets, sublimation printers, etc, but I am being very general here). So for most classical printers, a grid of "dots" build the halftoning pattern that creates the shades used to represent your pixels.
If this is such a printer, it is pointless to resolve the image down to the DPI of the printer. Even half is pushing it. I would suggest 100 PPI is enough for such 300 DPI printer.
As a matter of fact many professional printers are rated in LPI, which really is the "repetition rate" of the halftone pattern. Mind you, halftone dots can be split in half, so the "effective resolution" can be higher than the halftone pattern size, but not really much larger, and it can really only resolve edges better than the halftone pattern size, not micro-detail in any meaningful way.
Basically, if the actual resolution of your printing device really is 2400 DPI (like some pro magazine printers) then, yes, you may need 300 PPI renderings. Maybe. If even then.
The sad part is that even the guys in charge of handling the print stuff rarely understands the difference between DPI, LPI and PPI.
Not to mention that they tell you "This image should be 10 inches by 5 inches, at 300 DPI", and then you send them an image of 3000 by 1500 pixels, they get back to you and say "Hey, your image was 72DPI and way too big, you must re-render it..... we can't use it!"
/Z