You can do simpler than using Chebyshev’s inequality : the distribution of $\sum_{i=1}^n X_i^2$ under $H_0$ known, it is a $\chi^2(n)$. From this you can get a threshold $t_\alpha$, using simply a chi square table.
This is a particularly simple situation as the variance of the law under $H_0$ in known. This is almost like the kind of artificial stuff I teach to beginners, I would be pleased if you were kind enough to describe the concrete situation that lead you to this model.