There is a significant problem with using bands for assistance on chin-ups. What they actually give is the most help at the start of the exercise. This is needless as it is more than likely where you are strongest. The limiting factor in chin-ups and pull-ups is strength at the mid and top range of motion, and so this tool does not provide the appropriate stimulus. It also further justifies the need for isometric holds at the top range and for later down the line in your programming at mid range. Using bands on hanging pull exercises runs against the strength curve of the exercise and so this means the use of bands is ineffective and your time can be utilised better elsewhere.
It would be much more effective to learn how to utilise the eccentric component of your muscle contractions and use this to build up your concentric strength. As mentioned in the former, adding isometrics in your weakest positions are good methods for overload.
What I'd recommend doing:
After testing a clients upper body structural balance scores, if the client scores poorly on external rotator and scapular retractor scores, a smart approach would be to move in to cycles of training that focus on rowing exercises in contrast to vertical pulling ones. This is because your strength output would become better and vertical pulling promotes internal rotation of the shoulder. Even more so a reason to have good scapular retractors and external rotators when executing a vertical pull, (your chin up!)
Cycles of programming that include various seated rows with different hand placements and pulls such as the extended rope face pull with external rotation, that I must add is a favourite of mine, as it trains both the scapular retractors and the external rotators at the same time are great additions to your preparation phases of programming. With a little work on the shoulder girdle it will start hitting better positions as the retractors and rotators increase in strength. This is whilst the anterior muscles learn to open up for your benefit too.
Another area of weakness on clients when trying to perform good chin ups are the biceps. Including direct arm work within these phases will also aid your quest in achieving solid chin ups. Elbow flexor strength also must be made a priority. There is a direct link between a healthy shoulder girdle and a good set of 'gunz!'
Whilst doing all this your grip strength will also develop!
Next time your trying to improve your chin, throw away the band and work on your structural weaknesses, you'll have a great chin in no time!