Yes, you can have both. This is assuming, of course, that you will have a US SSN (or ITIN) and an address there. I have both the Canadian and the US version right now. But you will have trouble getting a US Chase card with no US credit history. Try for a different card first and move up to Chase once you've established a good credit history.

My first US card was a Capital One and my husbands was a Discover card. We had been turned down several times before that due to the lack of credit history. Once we got that first card, we put $50-ish on it every month, paid it off, repeat. After 3 months, I applied for a Chase card and was approved after calling in to to recon and faxing in copies of id documents to them. That was 2 years ago and once the floodgates were open, I have been approved for every card I've applied for since then and have a Fico score of almost 800. I have no US income and no visa (working visa, that is).

Chase Canada and Chase US are completely separate so you can't migrate to a US card but I believe American Express will transfer your Canadian credit history to the US. Others here will chime in on that, I'm sure. But once you establish a good credit history, you can definitely have both versions of the Marriott card.