The Atacama Large Millimeter/submillimeter Array (ALMA) is a general purpose telescope that performs a broad program of astrophysical observations. Beginning in late 2016, solar observations with ALMA became available, thereby opening a new window onto solar physics. Since then, the number of solar observing capabilities has increased substantially but polarimetric observations, a community priority, have not been available. Weakly circularly polarized emission is expected from the chromosphere where magnetic fields are strong. Hence, maps of Stokes V provide critical new constraints on the longitudinal component of the chromospheric magnetic field. Between 2019 and 2022, an ALMA solar development effort dedicated to making solar polarimetry at millimeter wavelengths a reality was carried out. Here, we discuss the development effort to enable solar polarimetry in the 3 mm band (ALMA Band 3) in detail and present a number of results that emerge from the development program. These include tests that validate polarization calibration, including evaluation of instrumental polarization: both antenna-based "leakage" terms and off-axis effects (termed "beam squint" for Stokes V). We also present test polarimetric observations of a magnetized source on the Sun, the following sunspot in a solar active region, which shows a significant Stokes V signature in line with expectations. Finally, we provide some cautions and guidance to users contemplating the use of polarization observations with ALMA.