New Job, Can I Ask for a Week Off?

Dear Experts, I just started a new job a month ago. Unexpectedly, I have the chance to go on an all-expense paid vacation to St. Thomas. However, I'd need a week off from work. I obviously don't have any vacation time. Do you think I could ask them to let me go and owe them the time? I can't afford to take the week unpaid. It's the chance of a lifetime! What can I do? Our Twitter Advice Project (T.A.P.) is no longer an active campaign. To find an answer to the above question, please use the "Search" box in the right-hand column of this website.