Drill press chucks generally mount in one of 3 ways and 2 involve tapers. A taper consists of precisely machined male and female partial cone shapes that are so closely fitted they stick together when you put them together. Big old drill presses frequently had an internal Morse taper in the main shaft which you could put taper shank drill bits into, or could mount a chuck using an "arbor" that has a external (male) Morse taper on one end and a different external taper on the other end that fits into the chuck (usually some type of "Jacobs" taper depending on the chuck) If there's a rounded rectangular hole through the main shaft about 6-8" up, that's a sign you may have a drill press with an internal Morse taper. If you are lucky, the run-out is due to a bent arbor or worn out chuck jaws, both are easily and cheaply replaced. Otherwise, the bearings could need replacement, or the main shaft could be bent or worn. The second chuck mounting method is to have a male Jacobs taper on the end of the main shaft that the drill chuck is pressed onto, sometimes there is a threaded retaining ring as well. In this case, if the problem is not worn out chuck jaws or bent chuck body, then it's the shaft or bearings. The last chuck mounting method uses external threads on the end of the main shaft that the chuck threads on to, in my experience this is mostly seen on newer, smaller and cheaper drill presses. If you can figure out how to remove the chuck (spend the few dollars for the proper drift tool or wedges, improper removal can cause more problems) you can use an indicator on the main shaft end and find out where the run-out is coming from. If the manufacturer name and part# are visible on the chuck, Google may help you find the mounting method and taper