The concept of a Q-polynomial distance-regular graph (DRG) was introduced by Delsarte in 1973. Since then, this concept has been linked to other areas, such as coding theory, Lie theory, and differential geometry. The double affine Hecke algebra (DAHA) was introduced by Cherednik in 1992. The theory of the DAHA has been connected to many other areas of mathematics, such as algebraic geometry, Lie theory, and orthogonal polynomials. I have discovered a relationship between Q-polynomial DRG's and a certain DAHA of rank one. In this talk we will display a certain module for a DAHA of rank one. Using this module we will show how Q-polynomial DRG's and the DAHA are related.