  We present a detailed analysis of HARPS-N radial velocity observations of
K2-100, a young and active star in the Praesepe cluster, which hosts a
transiting planet with a period of 1.7 days. We model the activity-induced
radial velocity variations of the host star with a multi-dimensional Gaussian
Process framework and detect a planetary signal of $10.6 \pm 3.0 {\rm
m\,s^{-1}}$, which matches the transit ephemeris, and translates to a planet
mass of $21.8 \pm 6.2 M_\oplus$. We perform a suite of validation tests to
confirm that our detected signal is genuine. This is the first mass measurement
for a transiting planet in a young open cluster. The relatively low density of
the planet, $2.04^{+0.66}_{-0.61} {\rm g\,cm^{-3}}$, implies that K2-100b
retains a significant volatile envelope. We estimate that the planet is losing
its atmosphere at a rate of $10^{11}-10^{12}\,{\rm g\,s^{-1}}$ due to the high
level of radiation it receives from its host star.
