That's not an easy question to answer.
Your old drill was presumably made with non-metric threads. You need to (a) convert your measurement to a fractional inch size and (b) note the number of threads per inch then (c) find those numbers together on a chart listing standard thread sizes.
So if, for example, you measured the outside diameter as 12.7 mm and counted 16 threads per inch, 12.7 mm converts to half an inch. Looking on a thread chart you would see that a half inch BSF (British Standard Fine) thread has 16 threads per inch, so that would possibly be the thread you need on the back of the chuck.
It soon gets complicated though - as far as I know, nobody makes chucks to those old standards now, so you would be looking for a second hand one. Chucks are not always marked with the thread size, so anyone with an old chuck knocking around might not know what they have. But if you know what you need, some kind soul on here might have one, waiting to come in useful.
Note that I made my example easy by picking 12.7 mm. As far as I can see, 17.8 mm is bigger than 11/16" (17.462 mm) but nearly the next size up which is 45/64" (17.859 mm). Would anyone have made a chuck to fit on a 45/64" thread? I've no idea - did I say this quickly gets complicated?
Was the person who sold you the drill without a chuck quite pleased that you bought it?