The energy levels of hydrogen-like atoms and ions are accurately described by bound-state quantum electrodynamics (QED). hbox {He}^{+} ions have a doubly charged nucleus, which enhances the higher-order QED contributions and makes them interesting for precise tests of QED. Systematic effects that currently dominate the uncertainty in hydrogen spectroscopy, such as the second-order Doppler shift and time-of-flight broadening, are largely suppressed by performing spectroscopy on trapped and cooled hbox {He}^{+} ions. Measuring a transition in hbox {He}^{+} will extend the test of QED beyond the long-studied hydrogen. In this article, we describe our progress toward precision spectroscopy of the 1 S–2 S two-photon transition in hbox {He}^{+}. The transition can be excited by radiation at a wavelength of 60.8 nm generated by a high-power infrared frequency comb using high-order harmonic generation (HHG). The hbox {He}^{+} ions are trapped in a Paul trap and sympathetically cooled with laser-cooled hbox {Be}^{+} ions. Our recently developed signal detection scheme based on secular-scan spectrometry is capable of detecting hbox {He}^{+} excitation with single-event sensitivity.Graphic abstract