Hi Lois, I would not say there would be too much competition. The DL roots are shallow; the Clematis roots are deep. They have similar requirements: both need excellent drainage. I would go for it! Maybe, they would need some extra fertilizing during the growing season.

I've got clematis planted near my Daylilies and have had no problems..I cite what Alina said...good advice...Jeanne

Thanks so much for the advice. I knew I could count on you folks so I will go for it.
Lois