  Precision laser spectroscopy in the extreme ultraviolet of the 1S-2S
two-photon transition in singly-ionized helium is a promising route for tests
of fundamental physics. We demonstrate laser excitation of this transition in
an atomic beam of $^3$He, based on an amplified frequency comb pulse at 790 nm
combined with its 25$^{\text{th}}$ harmonic at 32 nm. A clear resonance is
observed with a maximum excitation probability of close to 10$^{-4}$ per pulse,
and the results are well described by our simulations. This paves the way for
high-precision Ramsey-comb spectroscopy of a single helium ion in a Paul trap.
