  In the pursuit of physics beyond the Standard Model, a promising path is the
study of B-meson decays caused by the transition $b \to s\ell^+\ell^-$. A key
observable in such decays is the ratio $R_K$, which measures electron--muon
universality in $B \to K \mu^+\mu^-/e^+e^-$. At first sight, the recent LHCb
measurement of $R_K \sim 1$ may seem to largely constrain deviations from
universality in these decays. However, we show that this is actually not the
case: new sources of CP violation allow for significant universality violation
consistent with $R_K \sim 1$. This provides an exciting new opportunity to
search for New Physics by measuring differences between CP asymmetries in $B
\to K\mu^+\mu^-$ and $B \to K e^+e^-$.
