Creating a Business in the US on an H1-B Visa?

GnaGnaGna asks: "I've lived in the US for almost a year now and have a full time position with a major American company under an H1-B visa (work visa for foreigners). Besides this job, I also run an increasingly popular website generating AdSense revenues. I am not sure if I am allowed to create a US company (most likely an LLC), under my legal status, and transfer the Adsense profits to my personal bank account or a business bank account. Have my fellow readers faced a similar legal situation or know anything about it?"