ubuntu: sound: send one application sound to left speaker and another to a right speaker
Solution 1:
One way would be to use the Jack sound server. It is a bit tough to use, but it gives you complete control on the connections between all the sound sources and sinks. Through this, you could direct the sound of Chrome to one channel of your sound card, and the sound from Rythmbox to the other one. Practically, you would need to route the outputs of each program to a jack port. Afterwards, the output of these ports can be connected to the left and right sinks of your sound card (generally alsa_pcm:playback_?). Check this article for an example of Jack usage. However, you will probably prefer using QJackCtl as Jack is hard to use in command line. With this program, the task of connecting audio inputs and outputs is piece of cake. Check this full article in the Linux Journal presenting the interface. You can see how stereo channels are broken down and connected to other sound sinks in Figure 11 of this article.
I cannot describe the procedure more precisely than this, as the exact names of the components to connect depend on your system.
Note that both Jackd and QJackCtl can be installed through repositories with most distributions.
I hope it helps!