  In this joint experimental and theoretical work magnetic properties of the
Cu$^{2+}$ mineral szenicsite Cu$_3$(MoO$_4$)(OH)$_4$ are investigated. This
compound features isolated triple chains in its crystal structure, where the
central chain involves an edge-sharing geometry of the CuO$_4$ plaquettes,
while the two side chains feature a corner-sharing zig-zag geometry. The
magnetism of the side chains can be described in terms of antiferromagnetic
dimers with a coupling larger than 200 K. The central chain was found to be a
realization of the frustrated antiferromagnetic $J_1$-$J_2$ chain model with
$J_1\simeq 68$ K and a sizable second-neighbor coupling $J_2$. The central and
side chains are nearly decoupled owing to interchain frustration. Therefore,
the low-temperature behavior of szenicsite should be entirely determined by the
physics of the central frustrated $J_1$-$J_2$ chain. Our heat-capacity
measurements reveal an accumulation of entropy at low temperatures and suggest
a proximity of the system to the Majumdar-Ghosh point of the antiferromagnetic
$J_1$-$J_2$ spin chain, $J_2/J_1=0.5$.
