We have identified 21 millisecond pulsars (MSPs) in globular cluster Terzan 5 by using the Green Bank Telescope, bringing the total of known MSPs in Terzan 5 to 24. These discoveries confirm fundamental predictions of globular cluster and binary system evolution. Thirteen of the new MSPs are in binaries, of which two show eclipses and two have highly eccentric orbits. The relativistic periastron advance for the two eccentric systems indicates that at least one of these pulsars has a mass 1.68 times greater than the mass of the Sun at 95% confidence. Such large neutron star masses constrain the equation of state of matter at or beyond the nuclear equilibrium density.