The chuck on a drill is often the first part to wear out or break. Luckily, replacing it is a fairly easy process that does not normally require disassembly of the drill.
Even if the spindle or gearbox of your drill needs replacing - which does require disassembly - it's best to remove the chuck before disassembling the housing.
This guide should help you to replace the chuck on almost any corded or cordless drill, as drill chucks are almost always attached to the spindle by a screw thread. By far the most common thread size is 1/2" x20tpi UNF, but smaller drills can have a 3/8" or even smaller thread.
In some rare cases such as angle drills, very old models or large machines, the chuck may be mounted on a tapered shank or it may even have a proprietary fitting requiring disassembly of the housing. In those cases, this guide is not applicable. When in doubt, refer to the technical documentation for your make and model.