The question of non-vanishing of \(L\)-functions at the central point is related to many deep arithmetical problems. A conjecture of Chowla states that \(L(\frac{1}{2},\chi)\) is non-zero for all Dirichlet \(L\)-functions \(L(s,\chi)\) of real primitive characters. In this talk, we consider the family of the Dirichlet \(L\)-functions \(L(s,\chi_p)\), where \(p\) varies over the primes congruent to 1 mod 8 and \(\chi_p\) is the real primitive Dirichlet character of conductor \(p\). We prove that more than nine percent of their central values are non-zero. Previously, it was not known whether a positive proportion of these central values are non-zero. This is joint work with Kyle Pratt.