  Two-dimensional superfluidity and quantum turbulence are directly connected
to the microscopic dynamics of quantized vortices. However, surface effects
have prevented direct observations of coherent vortex dynamics in
strongly-interacting two-dimensional systems. Here, we overcome this challenge
by confining a two-dimensional droplet of superfluid helium at microscale on
the atomically-smooth surface of a silicon chip. An on-chip optical microcavity
allows laser-initiation of vortex clusters and nondestructive observation of
their decay in a single shot. Coherent dynamics dominate, with thermal vortex
diffusion suppressed by six orders-of-magnitude. This establishes a new on-chip
platform to study emergent phenomena in strongly-interacting superfluids, test
astrophysical dynamics such as those in the superfluid core of neutron stars in
the laboratory, and construct quantum technologies such as precision inertial
sensors.
