Thanks. I have tried Gentle Alarm and Alarm Clock +, which does have a chime, but only on the hour.
UPDATE: In case anyone has the same need, my long search brought me to 1st Clock, which runs on Win7 64 bit. It's a no frills, developers' program, and because of this is customizable in every way. I have it set to sound a single beep at the quarter hour, between 9:00 a.m. and 8:00 p.m., M-F. I need this for my work. I could set up many other alarms, launch programs, etc. And not only is there a great selection of sounds, you can select what instrument, out of 20 or so, will play that sound, in addition to playing your own mp3s. I have just started the trial, but I'm sure I will pay the $30 in a few days.