  We compute the second Hochschild cohomology space $HH^2(\mathcal{H}_1)$ of
Connes-Moscovici's Hopf algebra $\mathcal{H}_1$, giving the infinitesimal
deformations (up to equivalence) of the associative structure.
  $HH^2(\mathcal{H}_1)$ is shown to be one dimensional, and thus
Connes-Moscovici's formal deformation of $\mathcal{H}_1$ using Rankin-Cohen
brackets is unique up to equivalence.
