  Jets present ubiquitously in both quiet and active regions on the Sun. They
are widely believed to be driven by magnetic reconnection. A fan-spine
structure has been frequently reported in some coronal jets and flares,
regarded as a signature of ongoing magnetic reconnection in a topology
consisting of a magnetic null connected by a fan-like separatrix surface and a
spine. However, for small-scale chromospheric jets, clear evidence of such
structures is rather rare, although they are implied in earlier works that show
an inverted-Y-shaped feature. Here we report high-resolution (0$"$.16)
observations of a small-scale chromospheric jet obtained by the New Solar
Telescope (NST) using 10830~{\AA} filtergrams. Bi-directional flows were
observed across the separatrix regions in the 10830~\AA{} images, suggesting
that the jet was produced due to magnetic reconnection. At the base of the jet,
a fan-spine structure was clearly resolved by the NST, including the spine and
the fan-like surface, as well as the loops before and after the reconnection. A
major part of this fan-spine structure, with the exception of its bright
footpoints and part of the base arc, was invisible in the extreme ultraviolet
and soft X-ray images (observed by the Atmosphere Imaging Assembly and the
X-Ray Telescope, respectively), indicating that the reconnection occurred in
the upper chromosphere. Our observations suggest that the evolution of this
chromospheric jet is consistent with a two-step reconnection scenario proposed
by \citet{Torok2009}
