Where are you checking the chuck for concentricity?
The O D does not matter, but how it holds a piece of KNOWN round bar does. Suggest holding a piece of inch diameter Silver Steel in the chuck (Make sure that the jaws are clean, where they grip the work).
It might be worth removing the jaws, and cleaning the chuck jaws where they engage the scroll. To try to avoid stripping the chuck, try holding an old, clean, toothbrush in one of the slots for a jaw, and rotating the scroll,with the chuck key, to brush any swarf out of the scroll, before refitting the cleaned jaws.
Then grip the Silver steel in the chuck, and clock it for concentricity, close to the jaws. A good 3 jaw would probably be within 5 thou T I R, but a worn / badly butchered one could be wildly out (Once saw one 0.036 inch T I R !)
The run out may well be different if you recheck with a different size bar in the chuck.
Howard