The Los Angeles Archdiocese released surveillance video of the man, and Los Angeles police hope the footage will help investigators.
The incident occurred sometime after 9 p.m. Tuesday at the chapel at St. Patrick's Church on Cahuenga Boulevard.
When the suspect couldn't open the tabernacle, he went after the chapel's statues and paintings, knocking them down.
The damage estimate was not immediately available.
If you recognize the man in the video, you're urged to contact the LAPD.