Prospects for a precision timing upgrade of the CMS PbWO$_4$ crystal electromagnetic calorimeter for the HL-LHC

Particle detectors with a timing resolution of order 10 ps can improve event reconstruction at high-luminosity hadron colliders tremendously. The upgrade of the Compact Muon Solenoid (CMS) crystal electromagnetic calorimeter (ECAL), which will operate at the High-Luminosity Large Hadron Collider (HL-LHC), will achieve a timing resolution of around 30 ps for high-energy photons and electrons. The benefits of precision timing for the ECAL event reconstruction at HL-LHC will be discussed in this presentation. Simulation and test beam studies carried out for the timing upgrade of the CMS ECAL will be presented and the prospects for a full implementation of this option will be discussed.