Can I assign programs to multiple sound outputs?

My computer has built in sound, it also has sound over HDMI.

The video playback software that came with my blueray drive recognizes the sound over HDMI, and gives me the option to use it, while everything else comes out the computer's speakers.

Can I do this with a single program? I'd REALLY like to set my VM to the sound over HDMI, but that's not the point here [but I'm open for ideas there!]

My main goal is to have one of my browsers [Chrome preferred] use the HDMI sound while the rest of the computer continues to use the standard sound output

You can only have one default audio playback device. You can't have some sound go to the PC's speakers and others go to the HDMI at the same time. It has to be one or the other.

You can with programs which allow you to choose which device to use in the options.
If there is no option, or the application does not allow you to choose the audio device, it will always use the default method.

To force everything through HDMI, Right click the volume icon, choose Playback Devices and set HDMI to Default. That's the only way to force everything through it.

If you want all of your audio automagically switched to HDMI when a particular program is running, Audio Output Switcher is a free little program that will do the job for you. I use it to switch my audio from my soundcard and speakers to the HDMI going to my TV whenever I have VLC running. When I close VLC, the audio switches back to the soundcard and speakers.