The elements germanium (Ge, Z=32), arsenic (As, Z=33), and selenium (Se, Z=34) span the transition from charged-particle or explosive synthesis of the iron-group elements to neutron-capture synthesis of heavier elements. Among these three elements, only the chemical evolution of germanium has been studied previously. Here we use archive observations made with the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope and observations from several ground-based facilities to study the chemical enrichment histories of seven stars with metallicities -2.6 < [Fe/H] < -0.4. We perform a standard abundance analysis of germanium, arsenic, selenium, and several other elements produced by neutron-capture reactions. When combined with previous derivations of germanium abundances in metal-poor stars, our sample reveals an increase in the [Ge/Fe] ratios at higher metallicities. This could mark the onset of the weak s-process contribution to germanium. In contrast, the [As/Fe] and [Se/Fe] ratios remain roughly constant. These data do not directly indicate the origin of germanium, arsenic, and selenium at low metallicity, but they suggest that the weak and main components of the s-process are not likely sources.