Its not clear if your losing your chuck key, or your looking for a place to keep it handy.
I wouldn,t want a chuck key on a bungee cord, and hanging anywhere near the chuck. Just dont trust a BC.
I have a wooden tray on top of my headstock that holds all my keys. I realize not all machines have a spot on the headstock to have a tray.
If its a case of your not wanting to leave it in the chuck, then you have other choices. Paint the key bright yellow if you misplace it often. that colour is about the most visable, other than maybe hot pink.:whistle:
You could tack weld a spring on your key, so it will allways self eject after each use. Some guys have those chuck hood that has a saftey switch installed, so if the key is in, and the hood is up, the saftey switch prevents the lathe from starting.
Depending on your setup, you could also make a mount for the front of your chip tray to hold all the keys you normally use.
Or the simple method, paint it a bright colour so you cant miss it, and remove it a toss it in your chip tray every time.
Id rather do any of the above before I would hang a key from a bungee cord.
As Purplev said, pratice,safe habits.