Actually, supplemental exercises are a whole other subject!
As to Barbell Curls, I think they can help you if performed correctly. How many times have you seen guys in the Gym working with a weight that's just to heavy for them? They then throw the entire upper body into the movement thus nullifying all the good.
I like strict Barbell Curls. In fact, if you don't trust yourself put your back against a wall, or post so that you won't be using upper body momentum instead of Bicep strength. Since you are not allowed to use any momentum when performing dead hang Chin-ups why use it when you train the biceps with other movements?
Depending on the schedule that I'm on I like four sets of Barbell curls always performed after your Chin-ups. I never go below 8 reps and on my last set I sometimes go as high as 15 or 20 reps. It might look like this: 8-8-8-20 (or some other similar variation). I am pushing the biceps on the last set (I drop the weight naturally) in order to completly fatigue them and get them used to performing while flush with lactic acid. The other sets are strength builders. Again, it depends on my schedule.
I also like close grip Chin-ups as a supplementary movement to regular dead hang Chin-ups. Place your hands on the bar so that they are no more than 6" apart. If you have never done this type of Chin-up you are in for a real treat (wink). It feels quite awkward at first because you are more or less shutting down the powerful back muscles in particularly the Latissimus Dorsi. It's you and your biceps!
If you are not used to this movement it will be quite challenging at first. But, as you get better at it you will see your normal (hand spacing) Chin-ups go through the roof in terms of reps!
These can be intense so I don't recommend that you perform any more than two sets at the end of your normal Chin routine. Make sure you rest a good 4:00 or so before taking them on. In fact, sometimes I will do them as the last two sets in my workout. Stop one or two reps short of failure. If you can only do one or two reps use a colored band to assist you.
There are other good supplemental movements, the two above are obviously just focused on the biceps.