  In this paper we investigate the inflationary phenomenology of an
Einstein-Gauss-Bonnet theory compatible with the GW170817 event, by imposing
the constant-roll evolution on the scalar field. We develop the constant-roll
GW170817-compatible Einstein-Gauss-Bonnet formalism, and we calculate the
slow-roll indices and the observational indices of inflation, for several
models of interest. As we demonstrate, the phenomenological viability of the
models we study is achieved for a wide range of the free parameters. In
addition, for the same values of the free parameters that guarantee the
inflationary phenomenological viability of the models, we also make predictions
for the non-Gaussianities of the models, since the constant-roll evolution is
known to enhance non-Gaussianities. As we show the non-Gaussianities are of the
same order for the slow-roll and constant-roll case, and in fact in some cases,
the amount of the non-Gaussianities is smaller in the constant-roll case.
