A researcher testing $H_0: \theta = 0$ against $H_a: \theta > 0$ uses the Score test. If the score function is $U(\theta) = \sum \frac{\partial}{\partial \theta} \ln f(X_i|\theta)$ and Fisher information is $I(\theta)$, what is the correct asymptotic distribution of the statistic $S = \frac{U(\theta_0)^2}{I(\theta_0)}$ as $n \to \infty$ under $H_0$?