Large values of $L(1,\chi)$ for quadratic Dirichlet characters $\chi$

Question

Granville and Soundararajan, in "Upper Bounds for $L(1, \chi)$", first paragraph, say it is known that there exist quadratic Dirichlet characters $\chi$ for which $L(1, \chi)$ is about $\log\log q$, where $q$ is the conductor of $\chi$. Those authors gave no reference, and I can't find one so far. Can anyone point me to a reference?