Can I work for the other employer?

Hi THere,

I just got an offer, I am thinking of quitting the current job. But since I have accrued some vacation time on the current job, I am thinking of quitting the job and taking the vacation time off, and in the same time I can start to work for the new employer. Right now I am on H1b visa, the second employer will do the H1B visa for me soon. So I do not know if this is against law.

Any idea will be greatly appreciated!