It's impossible to diagnose a printing problem, if you don't give more details about the file and your printing environment. That would help determine if its a system problem or an application problem or a file problem.
How is it connected to your computer? Directly or networked (wireless)?
Is it just this one file or can you print at all to the hp?
First thing that comes to my mind would be drivers. Do you have the correct drivers (OSX) for your printer installed? I know from experience that hp is one of the worst in regard of supplying updated printer drivers for Mac OSX.
Next would be the contents of the file. Fonts for example. If there is live type in the file. convert to outlines and try again.
Make sure your Illustrator document is in CMYK mode.
Can you print the file when placed in a layout program?