For the task a lathe is needed.
The chuck is new and I could have asked for it to be replaced with a new one, but I believe it wasn't worth because of the shipping costs, (I live in Italy and I ordered it from the US), then this is an inexpensive chuck and probably a new chuck would have not performed much better than this one.
So I tried to do it by myself.
If it didn't work, I would have bought a new, and better quality chuck for this nice drill.

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