The September 1 1931 edition of the Toronto Daily Star contained several ads that looked like this:

The radio page of that day’s edition provided an answer to the mystery:

Looking at that day’s radio listings revealed that the show was literally called the Three Star Programme:

Some of the other listings are intriguing. Pianomania? Hungry five? A choice between sacred songs and a dinner dance?
Unfortunately, I couldn’t find out anything about the Three Star Programme. I did find a link to an episode of Daddy and Rollo, a program that was running at the same time. Rex Battle, being broadcast on CPRY, has appeared in this blog before.