  Using data from JWST, we analyze the compact sources ("sparkles") located
around a remarkable $z_{\rm spec}=1.378$ galaxy (the "Sparkler") that is
strongly gravitationally lensed by the $z=0.39$ galaxy cluster SMACS
J0723.3-7327. Several of these compact sources can be cross-identified in
multiple images, making it clear that they are associated with the host galaxy.
Combining data from JWST's {\em Near-Infrared Camera} (NIRCam) with archival
data from the {\em Hubble Space Telescope} (HST), we perform 0.4-4.4$\mu$m
photometry on these objects, finding several of them to be very red and
consistent with the colors of quenched, old stellar systems. Morphological fits
confirm that these red sources are spatially unresolved even in strongly
magnified JWST/NIRCam images, while JWST/NIRISS spectra show [OIII]5007
emission in the body of the Sparkler but no indication of star formation in the
red compact sparkles. The most natural interpretation of these compact red
companions to the Sparkler is that they are evolved globular clusters seen at
$z=1.378$. Applying \textsc{Dense Basis} SED-fitting to the sample, we infer
formation redshifts of $z_{form} \sim 7-11$ for these globular cluster
candidates, corresponding to ages of $\sim 3.9-4.1$ Gyr at the epoch of
observation and a formation time just $\sim$0.5~Gyr after the Big Bang. If
confirmed with additional spectroscopy, these red, compact "sparkles" represent
the first evolved globular clusters found at high redshift, could be amongst
the earliest observed objects to have quenched their star formation in the
Universe, and may open a new window into understanding globular cluster
formation. Data and code to reproduce our results will be made available at
\faGithub\href{https://niriss.github.io/sparkler.html}{http://canucs-jwst.com/sparkler.html}.
