  We study zero distribution of random linear combinations of the form
$$P_n(z)=\sum_{j=0}^n\eta_j\phi_j(z),$$ in any Jordan region $\Omega \subset
\mathbb C$. The basis functions $\phi_j$ are orthogonal polynomials on the unit
circle (OPUC) that are real-valued on the real line, and $\eta_0,\dots,\eta_n$
are complex-valued iid Gaussian random variables. We derive an explicit
intensity function for the number of zeros of $P_n$ in $\Omega$ for each fixed
$n$. Using the Christoffel-Darboux formula, the intensity function takes a very
simple shape. Moreover, we give the limiting value of the intensity function
when the orthogonal polynomials are associated to Szeg\H{o} weights.
