  In this paper we review the recent discovery of several millisecond pulsars
(MSPs) in eccentric binary systems. Timing these MSPs we were able to estimate
(and in one case precisely measure) their masses. These results suggest that,
as a class, MSPs have a much wider range of masses (1.3 to > 2 solar masses)
than the normal and mildly recycled pulsars found in double neutron star (DNS)
systems (1.25 < Mp < 1.44 solar masses). This is very likely to be due to the
prolonged accretion episode that is thought to be required to form a MSP. The
likely existence of massive MSPs makes them a powerful probe for understanding
the behavior of matter at densities larger than that of the atomic nucleus; in
particular, the precise measurement of the mass of PSR J1903+0327 ($1.67 +/-
0.01 solar masses) excludes several "soft" equations of state for dense matter.
