I've done that a few times over the years. Easy with a drill press, but can be done with just a drill as well, if you are careful with measurements on each side.

 

BTW....if you dislike the look of the regular ones...I have tried chrome and it rusts. I found on Amazon an aluminum one... it will look nicer and also prob be easier to drill.

 

Off topic, but do you leave yours on? I'm of the mindset to remove mine pretty much as quick as I disconnect the trailer. The only time in life I didn't do that was when towing a large trailer on a daily basis. Then I added grease occasionally to the ball, which didn't go well with my father when his pants would make contact. We were towing enough with multiple vehicles that we would have to replace the ball every year or so, and also the hitch on the trailer as well. That portion required some welding, but no big deal as a construction company. Still, on weekends that hitch was removed.

I've never tried aluminum because I can't see how they can possibly be as strong as steel. I'm had some steel ones bend under heavy load, but every aluminum product I've ever worked with is fine, until it cracks and completely separates. That is of course what the chains are for, but I prefer to avoid that after millions of miles of trailer towing.

In the LR3/LR4 forums, it appears some people leave the hitch on all the time, then wonder why they can't remove it after rust happens.

 

I used to take mine off as soon as I was done towing, as they get nasty looking after time with rust etc. But the aluminum is shiny and since it is formed from one piece of alum block I bet they are actually stronger than a mutiple piece hitch. Now I don't mind leaving it on since it is actually good looking.
I have bought a couple of these for my various vehicles...Pair it with a stainless ball and it's practically a work of art.