  We treat the question of base-change in $THH$ for faithful Galois extensions
of ring spectra in the sense of Rognes. Given a faithful Galois extension $A
\to B$ of ring spectra, we consider whether the map $THH(A) \otimes_A B \to
THH(B)$ is an equivalence. We reprove and extend positive results of
Weibel-Geller and McCarthy-Minasian and offer new examples of Galois extensions
for which base-change holds. We also provide a counterexample where base-change
fails.
