Rule of thumb, up to 3.5x diameter sticking out of the chuck unsupported should be OK. Over 5x diameter is asking for trouble. Depends on the material, so I engage brain if sticking out more than 2.5x. How much of the job is gripped by the jaws is important; a thin rod completely gripped by the full length of the jaws is considerably safer than a fat rod gripped only by the far end of a set of reversed jaws. If it looks or feels dodgy, it is!
As Barrie says, long jobs usually need to be supported by a fixed and/or travelling steady because they bend so much.
I'd follow Barrie's step-at-a-time approach, ideally going down to 4mm in one cut if the lathe can manage it. (JasonB told me this one!) It's because a rod's ability to resist sideways forces depends on how thick it is – a 6mm diameter rod is far more easily bent than a 9mm rod.
I'd also consider holding the rod in a collet rather than a chuck because collets have less run-out. Each time the rod is advanced and retightened in a 3-jaw chuck is an opportunity for run-out to change the axis slightly and leave a visible ring at each step. A really poor chuck will make a mess of it! A really good one might not be a problem, or leave rings that can be quickly polished out.
As jobs go turning long slender rods is tricky. Don't be disheartened if it takes a few goes to get right.
Dave