Good question, Dawn.
The short answer to your question is
award-winning, but I suspect you could probably use
award winning and not be accused of having made an error.
Compound words and how they relate to hyphens tends to be in a state of flux depending on what source you refer to. The
Blue Book of Grammar and Punctuation advises to look words up in the dictionary in order to determine whether they are hyphenated. On that basis, Dictionary.com lists
award-winning as hyphenated as does a
Wikipedia article regarding hyphens.
Good luck!