  Axion-Like Particles (ALPs) are a generic, calculable, and well motivated
extension of the Standard Model with far reaching phenomenology. ALPs that
couple only to hypercharge represent one subset of such models, coupling the
ALP to both photons and the $Z$ boson. We examine the current constraints on
this class of models with an ALP mass in the 100 MeV to 100 GeV range, paying
particular attention to the region between 100 MeV to 10 GeV, a portion of
parameter space which is ill constrained by current experiments. We show that
the more than $10^{9}$ $Z$ bosons produced in the Giga-Z mode of the future ILC
experiment, combined with the highly granular nature of its detectors, will
allow for ALPs coupled to hypercharge to be discovered with couplings down to
nearly $10^{-5}\,\rm{GeV^{-1}}$ over a range of masses from 0.4 to 50 GeV.
