I have a Giant Aluxx frame with a Campy Centaur 10sp rear wheel and a 30-year-old Huret Jubilee rear derailler. No front shifter and only a 53-tooth Shimano 600 chainring. I use a bar-end to shift the rear. Rear cogs are 12-28 approx.

Very often when I shift the chain falls off the front ring. Either insider or outside. Going fast or slow. Shifting quick or gently. No particular cog. I can't figure it out.

I've tried shortening the chain and also max-tensioning the rear derailler. No improvement.

Any ideas for a simple cure other than installing a front derailler or some sort of chain-keeper?

(I don't notice that my chain hits my front derailler on my other bikes, or that they're trying to derail but are prevented by something. So it's hard to imagine that a front der would be the wonder cure for my problem. Maybe it's my primitive 1970's rear derailler