  Let $F$ be a linear combination of $N\geq 1$ Dirichlet $L$-functions attached
to even (or odd) primitive characters with the same modulus. Selberg proved
that a positive proportion of non-trivial zeros of $F$ lie on the critical
line. Our work here is to provide an explicit lower bound for this proportion.
In particular, we show that the lower bound $2.16\times 10^{-6}/(N\log N)$ is
admissible for large $N$.
