  Antihydrogen, the lightest atom consisting purely of antimatter, is an ideal
laboratory to study the CPT symmetry by comparison to hydrogen. With respect to
absolute precision, transitions within the ground-state hyperfine structure
(GS-HFS) are most appealing by virtue of their small energy separation. ASACUSA
proposed employing a beam of cold antihydrogen atoms in a Rabi-type experiment
to determine the GS-HFS in a field-free region. Here we present a measurement
of the zero-field hydrogen GS-HFS using the spectroscopy apparatus of ASACUSA's
antihydrogen experiment. The measured value of
$\nu_\mathrm{HF}$=$1~420~405~748.4(3.4)(1.6)~\textrm{Hz}$ with a relative
precision of $\Delta$$\nu_\mathrm{HF}$/$\nu_\mathrm{HF}$=$2.7\times10^{-9}$
constitutes the most precise determination of this quantity in a beam and
verifies the developed spectroscopy methods for the antihydrogen HFS experiment
to the ppb level. Together with the recently presented observation of
antihydrogen atoms $2.7~\textrm{m}$ downstream of the production region, the
prerequisites for a measurement with antihydrogen are now available within the
ASACUSA collaboration.
