You can use Pavel's "grease the groove" method and do a few reps (short of failure at all times, 2-3 reps in reserve) throughout the day on a daily basis. I've done that before. Every time I walked by the chin bar, I knocked out a set of 4-5 reps. I'd do this anywhere from 2-10 times in a day each day. I never trained to failure, I never did numerous sets in a row.
It works pretty good.
Otherwise, you could try to set up your training along the lines of Chad Waterbury's "100 Reps" program, but chins might not be the best exercise to do for that since it's a very difficult movement and works more than one muscle group.
What Nate suggested is that you do 4-5 reps per set. Spread the sets out throughout the day, and while the total volume is going to be up there, you're not going to failure each set, and you're recovering between the sets throughout the day. The most important aspect of recovery is neurological. If you're eating right and getting plenty of rest, you should gain size.
Of course, if you want a big back, you should be doing horizontal rows as well as vertical. I personally wouldn't do so much vertical. I would alternate vertical with horizontal. Also, alternate pull-ups with chin-ups.
The one problem I had after doing so many chins (besides a bigger back) was a muscle imblance from not doing enough rows and some shoulder pain later down the road.
However, I did a lot of rows, snatches, cleans and deadlifts to help counteract all the chinning, and I also eased up on the chin work.
But I had done all this chinning throughout an entire year, as my back was a weak spot. But now, my back is one of my best bodyparts. I have backed off (no pun intended) on back work and only do chins one day and rows another.
If you do it as listed (a few reps, throughout the day, each day), then you will get stronger and add some size. just don't forget to do some rowing and other stuff during your regular workouts.
If you feel like you're getting burned out or creating an imbalance, back off! If trying to focus on your chins, this method works to increase your strength and the amount of reps you'll be able to do.
If training in the gym three days a week, I'd suggest doing a full-body workout like Chad Waterbury's Total Body Training, Total Triple Training, The Waterbury Method, Lift Fast Get Big, Hybrid Hypertrophy or something along those lines.
You could use one of those programs to hit your entire body and then do the chinning at home each day (I'd take at least one or two full days off). This way, you can still make gains all over, but increase your chinning prowess (both strength and size).
I'm saying that you should weight train using full-body workouts three times a week. Also, you can do some extra chinning work at home as often as you want. However, I would take AT LEAST one full day off from all weight training and chinning. So maybe weight train on Mon, Wed, Fri and do your extra chins on Mon-Sat, but take Sunday off completely.
You'll have to go by how you feel. If you are burned out from the weight training, you may not be able to do all the extra chinning. Or, if your workouts suffer from the extra chinning, you may need to cut back as well.