It'll work fine. If you have a debit card with no chip, you may not be able to run it as a debit card (it'll run as credit, meaning you can't use it at Costco or places who only accept debit).
I'm in Canada for the summer and I learned that the hard way- I have to use cash at Costco, and there's a discount supermarket that only accepts debit and MasterCard- all I have with me is Visa/Amex/Discover, and my debit card has no chip so I can't use it at either of those places.