  We examine the constraining power of current gravitational-wave data on
scalar-tensor-Gauss-Bonnet theories that allow for the spontaneous
scalarization of black holes. In the fiducial model that we consider, a slowly
rotating black hole must scalarize if its size is comparable to the new length
scale $\lambda$ that the theory introduces, although rapidly rotating black
holes of any mass are effectively indistinguishable from their counterparts in
general relativity. With this in mind, we use the gravitational-wave event
GW190814$\,\unicode{x2014}\,$whose primary black hole has a spin that is
bounded to be small, and whose signal shows no evidence of a scalarized
primary$\,\unicode{x2014}\,$to rule out a narrow region of the parameter space.
In particular, we find that values of ${\lambda \in [56, 96]~M_\odot}$ are
strongly disfavored with a Bayes factor of $0.1$ or less. We also include a
second event, GW151226, in our analysis to illustrate what information can be
extracted when the spins of both components are poorly measured.
