South Bend 9a new gap between chuck plate and spindle

Maybe take the chuck off the back plate, check runout of the backplate.
Re fit the chuck if you have to?
EDIT I have a SB 9 also, have fitted a couple chucks to back plates and they run very true.
 
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This is a lesson on ensuring that your chuck threads are clean before you put it on. The fact that the 3-jaw was "a real drill" to remove leads me to believe that it, too, had chips in the threads.

The OP is lucky. Chips in the chuck threads can make removal of the chuck nearly impossible, especially if the chuck had difficulty going on. Stuck chucks have had to be TURNED off to recover usage of the lathe.

A chuck should easily spin on it's intended lathe. If there seems to be resistance, remove the chuck and clean the threads again. A 3-jaw can hold chips hidden from view and fall out while it is spinning on. A really dirty chuck should be disassembled and thoroughly cleaned before use. Run the spindle in reverse and put a toothbrush on its threads to clean it up, too.
 
Even after you have done your best, I think you only finally drive it home if you regrind the jaws to eliminate "bell mouth wear". There is a ton of videos on YT on how to do it, using every kind of router, Dremmel, apparently anything with a motor, and at least one strapped to a plywood jig with cable ties. Also, various trick ways to hold the jaws open, disc in the back, wide rings, etc.

Stopping the grinding dust getting where it shouldn't would be a problem, and I have not yet attempted such, although I must admit, I have thought about it. So far, for me, I am happy to carefully and completely clean, lubricate, and re-assemble the chuck(s), and the threads they go on.

I am going to invest some time and quality marine ply into making up chuck carrier holders with handles that can sit on the ways, and allow the chuck to be offered up for threading onto the spindle. The dings I can see probably came from dropping a chuck.
 
Update on this: The chuck is mounted on the back plate with 3 screws and therefore only 3 combinations. The best was 3 thou runout as measured with a dial indicator and a section of drill rod.
I then remove the chuck and mounted the drill rod to the spindle via a collet. This measured less than but close to a thou. It would seam that there is some runout in the spindle.
I do not see a way to improve the chuck.
 
dansawyer said:
The best was 3 thou runout as measured with a dial indicator and a section of drill rod. I do not see a way to improve the chuck.
Click to expand...

Did you face the back plate before you put on the chuck? Also, just because there are holes in the BP doesn't mean you have to use those. Just put in three new holes.
 
Check the spindle without the chuck. Discover if the face the chuck will mate with has run-out. Even if it has, it need not be a problem if you face the back-plate while on the spindle.

Check also for radial run-out on the spindle - just in case it is something to do with the spindle bearing. A bit far-fetched, but you should be able to get to the point where you know exactly the state of all measures and alignments, and then choose a fix.
 
Thank you all for your input, it is helpful I have done extra testing.
First, after removing the chuck the spindle itself is good. The inside edge where an MT3 collet would sit is on the order of half a thou.
Second, the outer lip of the spindle where the chuck would mate is also on the order of half a thou.
Third, placing a drill rod in a collet in the spindle shows just over one thou on the drill rod. This could be either the from the collet or the rod itself.
Finally, after cleaning the chuck and spindle threads and carefully seating the chuck the drill rod measures about 2 thou.
Based on the above I am assuming the run-out is the sum of the spindle, the chuck, and the drill rod itself. My next step is to take a piece of rod and carefully remove a small amount and check for equal radius round and end to end. The proof of the pudding ...
 
dansawyer said:
My next step is to take a piece of rod and carefully remove a small amount and check for equal radius round and end to end. The proof of the pudding ...
Click to expand...

All this will do is hide the runout. Repeat the runout test with the drill rod in the chuck. Mark the "highest" point with a Sharpie on both the chuck and the rod. Now rotate the drill rod in the chuck 90º and repeat. If the mark is in the same place on the chuck, the problem is with the chuck. If it moves with the rod, the problem is with the rod.
 
dansawyer said:
Finally, after cleaning the chuck and spindle threads and carefully seating the chuck the drill rod measures about 2 thou.
Click to expand...

This is as good as you can reasonably expect from a 3-jaw unless it's an Adjust-Tru. Trying to get it closer is doomed to failure.
 
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