Cool stars like the Sun show chromospheric activity, which is largely attributed to nonradiative sources of energy linked to rotationally driven magnetic fields. However, a nonmagnetic process, such as dissipation of acoustic waves, may operate side by side with the first process. We report detections of chromospheric emission reversals in Mg II 2800 A spectra for nine metal-poor solar-type stars, some believed to be among the oldest stars known, whose great age and slow rotation argue against strong magnetic activity. Although interstellar absorption is always present, in seven stars with high radial velocities each reversal profile is seen to be doubly peaked, with the blue peak stronger than the red, much like such profiles from the quiet Sun. Despite having as little as 1/300th as much metal as the Sun and being 3 times as old, these stars have chromospheric activity comparable to that in solar quiet regions. While these data do not rule out magnetic fields, they support an acoustic origin of chromospheric emission and show that relatively inactive solar-type stars of all ages have chromospheres whose characteristics are largely independent of metallicity.