My chain has a tendency to frequently jump off the front chainring. I have a 1x9 so it's not a front derailleur issue. It generally happens when I hit something like the lip of a driveway or sidewalk at a crosswalk, which sucks when it pops off in the middle of crossing a busy highway in town. Could my chain be a bit too loose?
Is your front chainring on the outside or inside of the spider? Is it a converted 1x9 or did you purchase it as a 1x9?
It's most likely happening when you hit large bumps or holes in the road. It's possible that your chain is too long if you converted it from a 2x9 and didn't reduce the number of links in the chain.
If you converted it, it's also possible that the chainring is just too far away from your center line for a proper chainline when you're on your largest cog. If possible, move your chainring to the inner side of the spider. If you have a single ring crank, you may need to get a shorter BB/spindle.
Another cheaper and easier solution is to get a chain watcher. There are several types and brands such as N-stop, K-edge, Paul Components. This will sit on the inside and/or over the top of your chain on the front chainring which will help prevent the chain from jumping off the front ring. They are used widely in the cyclocross world to prevent this.