  We present an extensive experimental and theoretical study on the
low-temperature magnetic properties of the monoclinic anhydrous alum compound
BaMo(PO$_4$)$_2$. The magnetic susceptibility reveals strong antiferromagnetic
interactions $\theta_{CW} = -167$~K and long-range magnetic order at
$T_N=22$~K, in agreement with a recent report. Powder neutron diffraction
furthermore shows that the order is collinear, with the moments near the $ac$
plane. Neutron spectroscopy reveals a large excitation gap $\Delta = 15$~meV in
the low-temperature ordered phase, suggesting a much larger easy-axis spin
anisotropy than anticipated. However, the large anisotropy justifies the
relatively high ordered moment, N\'{e}el temperature, and collinear order
observed experimentally, and is furthermore reproduced in a first principles
calculations using a new computational scheme. We therefore propose
BaMo(PO$_4$)$_2$ to host $S=1$ antiferromagnetic chains with large easy-axis
anisotropy, which has been theoretically predicted to realize novel excitation
continua.
