The Last of Mrs. Cheyney is scheduled to air on TCM at 6:45am on June 13th, 2011. This is according to the Turner Classic Movies website. As always, check your local listings to make sure the date and time are correct.
I recorded it and just looked at it last night. It was a delightful movie. Norma Shearer was wonderful and I thought Basil Rathbone was equally good in a romantic role. I had never seen him as a romantic lead before - always the heavy or Sherlock Holmes.