  The RADiCAL Collaboration is conducting R\&D on high performance
electromagnetic (EM) calorimetry to address the challenges expected in future
collider experiments under conditions of high luminosity and/or high
irradiation (FCC-ee, FCC-hh and fixed target and forward physics environments).
Under development is a sampling calorimeter approach, known as RADiCAL modules,
based on scintillation and wavelength-shifting (WLS) technologies and
photosensor, including SiPM and SiPM-like technology. The modules discussed
herein consist of alternating layers of very dense (W) absorber and
scintillating crystal (LYSO:Ce) plates, assembled to a depth of 25 $X_0$. The
scintillation signals produced by the EM showers in the region of EM shower
maximum (shower max) are transmitted to SiPM located at the upstream and
downstream ends of the modules via quartz capillaries which penetrate the full
length of the module. The capillaries contain DSB1 organic plastic WLS
filaments positioned within the region of shower max, where the shower energy
deposition is greatest, and fused with quartz rod elsewhere. The wavelength
shifted light from this spatially-localized shower max region is then
propagated to the photosensors. This paper presents the results of an initial
measurement of the time resolution of a RADiCAL module over the energy range 25
GeV $\leq$ E $\leq$ 150 GeV using the H2 electron beam at CERN. The data
indicate an energy dependence of the time resolution that follows the
functional form: $\sigma_{t} = a/\sqrt{E} \oplus b$, where a = 256
$\sqrt{GeV}$~ps and b = 17.5 ps. The time resolution measured at the highest
electron beam energy for which data was currently recorded (150 GeV) was found
to be $\sigma_{t}$ = 27 ps.
