  Let $X(D,1) =\Gamma(D,1) \backslash \mathbb{H}$ denote the Shimura curve of
level $N=1$ arising from an indefinite quaternion algebra of fixed discriminant
$D$. We study the discrete average of the error term in the hyperbolic circle
problem over Heegner points of discriminant $d <0$ on $X(D,1)$ as $d \to
-\infty$. We prove that if $|d|$ is sufficiently large compared to the radius
$r \approx \log X$ of the circle, we can improve on the classical
$O(X^{2/3})$-bound of Selberg. Our result extends the result of Petridis and
Risager for the modular surface to arithmetic compact Riemann surfaces.
