  We evaluate the variance of the number of lattice points in a small randomly
rotated spherical ball on a surface of 3-dimensional sphere centered at the
origin. Previously, Bourgain, Rudnick, and Sarnak showed conditionally on the
Generalized Lindel\"of Hypothesis that the variance is bounded from above by
$\sigma(\Omega_n){N_n}^{1+\varepsilon}$, where $\sigma(\Omega_n)$ is the area
of the ball $\Omega_n$ on the unit sphere, $N_n$ is the total number of
solutions of Diophantine equation $x^2 + y^2 + z^2 = n$. Assuming the Grand
Riemann Hypothesis and using the moments method of Soundararajan and Harper, we
establish the upper bound of the form $c\sigma(\Omega_n) N_n$, where $c$ is an
absolute constant. This bound is of the conjectured order of magnitude.
