$^3$He-rich solar energetic particle (SEP) events, which result from the acceleration of energetic particles in association with reconnection events on the Sun, are identified on the basis of 3He/4He enhancements of at least several orders of magnitude over the solar coronal value of ~0.04%. The ULEIS and SIS instruments on the Advanced Composition Explorer (ACE) have been measuring the occurrence of SEP $^3$He in the interplanetary medium near Earth over nearly two full solar cycles. The $^3$He isotope has been observed nearly 90% of the time at solar maximum, but no more than a few % of the time at solar minimum. NASA’s Parker Solar Probe (PSP) spacecraft was launched in August 2018 on a mission designed to include 24 close flybys of the Sun over seven years. PSP’s scientific objectives include the study of the acceleration and transport of $^3$He-rich SEPs, and the spacecraft carries a two-instrument suite, ISOIS, that has the capability to perform these studies. The first two orbits of PSP occurred under extremely quiet solar-minimum conditions, which will provide an opportunity to search for small $^3$He-rich SEP events in the previously unexplored region <0.2 AU from the Sun under conditions with extremely low energetic-particle backgrounds. We present an update of the long-term record of SEP $^3$He occurrence near 1 AU and, with this context, discuss some advances that can be expected from PSP.