My trainer thinks that I was probably spinning too fast for the gear - and I do admit that the whole shifting thing is a mystery to me - though I do understand how to do it. I just don't know what gear to be in when. This is the first time that the chain has fallen, and it was right after I attempted to shift. Practice makes perfect

I do understand what combination of gears to avoid - but it will take practice to learn what gears to use when... This may be at least a part of the problem, or not, time will tell. Thanks again for all of the comments and advice, it is appreciated!