H-1B status in US but working for a company in home country on the side

[hunmkv]

I have an H-1B visa in US, but I am considering working with a company in my home country on the side. Specifically, it would be the consulting service related to US market in a project. Details are still lacking, but if the project succeeds in the end I may get paid by this company. This company may do business with US customers, but is not a US company. I need to know whether it is legal for me to do so (preferably with legal references). If so, what are other implications? Thanks.   

[JoeF]

On your current H1, you can ONLY work for your employer. That's the fundamental basics of a work visa.

You can NOT work for anybody else, not for another US company, nor for some company abroad, not as employee and certainly not as freelancing consultant, as long as you are in the US in H1 status.