I make jewelry for a living and most local jewelry stores who does repairs should be able to drill a pearl for you to whatever size you need to go over a chain.
I drill pearls all the time and the biggest hassle with the do-it-yourself necklaces is that you want a hole in the pearl that fits over the chain, but not the clasp – so you don’t want a monstrous hole in the pearl.
Also, the bigger the hole drilled in a good pearl the more it potentially degrades the value of the pearl because you are creating a bigger exposed area to its interior, thereby potentially causing the nacre to chip.
Typically, fine pearls are strung onto silk with a knot in between. This is done so that the pearls do not rub against each other. Pearls delicate. I used to work in jewelry and I saw many beautiful pearls ruined by hairspray, etc. Rings with pearls typically showed the worst damage.
In short, if you are buying fine quality pearls, reconsider the chain.