Stock alignment

Scroll chucks are never exactly true over their full travel. The scroll is not a precision guide to the jaws even when new, and often worse if some previous operator used it a lot or abused it. Swarf in the scroll can also be a problem. I would take it apart and clean, inspect, and test it, so you know what you have.

Also, a set true type chuck will not be accurate or repeatable over it's entire travel. If you dial it in on a 1" part, then 1" parts should stay pretty close. But 2" parts can very likely be off, again because the scroll is not a precision piece. You have to reset the chuck for each diameter, and really for every new part put in the chuck if you are seeking high accuracy. That is why I just use my 4 jaw for almost every task. A set true three jaw is in reality just a three jaw being dialed in by a four jaw. I only really use my 3 jaw for chucking triangular or hexagon parts, or if I am doing a longer series of parts that do not need to be accurate.
 
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I'm with Bob, Richard. I would personally take the chuck apart and clean it. Chips and crud can definitely affect how accurately a jaw clamps on the part. I don't think it would cause the kind of inaccuracy you are seeing but it contributes. With that said, having a hole come out as far off as your hole is, I am guessing the issue is not just the chuck but the drill itself or whatever is holding the drill.

Is the tailstock aligned with the spindle axis? Is the tailstock taper clean and in decent shape? Is the drill chuck mounted accurately on a decent arbor?

If the chuck was at fault, the hole would come out larger and out of round but for the hole to come out off axis ... that is on the drill end, not the chuck end.
 
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