  The most massive neutron stars constrain the behavior of ultra-dense matter,
with larger masses possible only for increasingly stiff equations of state.
Here, we present evidence that the black widow pulsar, PSR B1957+20, has a high
mass. We took spectra of its strongly irradiated companion and found an
observed radial-velocity amplitude of K_obs=324+/-3 km/s. Correcting this for
the fact that, due to the irradiation, the center of light lies inward relative
to the center of mass, we infer a true radial-velocity amplitude of K_2=353+/-4
km/s and a mass ratio q=M_PSR/M_2=69.2+/-0.8. Combined with the inclination
i=65+/-2 deg inferred from models of the lightcurve, our best-fit pulsar mass
is M_PSR=2.40+/-0.12 M_sun. We discuss possible systematic uncertainties, in
particular in the lightcurve modeling. Taking an upper limit of i<85 deg based
on the absence of radio eclipses at high frequency, combined with a
conservative lower-limit to the motion of the center of mass, K_2>343 km/s
(q>67.3), we infer a lower limit to the pulsar mass of M_PSR>1.66 M_sun.
