Using data from JWST, we analyse the compact sources ("sparkles") located around a remarkable z(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 JWSTs Near-Infrared Camera (NIRCam) with archival data from the Hubble Space Telescope (HST), we perform 0.1 1.4 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 the strongly magnified JWST/NIRCam images, while the JWST/NIRISS spectra show [OIII] lambda 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 DENSE BASIS spectral energy distribution fitting to the sample, we infer formation redshifts of z(form) similar to 7-11 for these globular cluster candidates, corresponding to ages of similar to 3.9-4.1 Gyr at the epoch of observation and a formation time just similar to 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, which could be among 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 http://canucs-jwst.com/sparkler.html.