Be very, very careful if you are feeling elbow tendon pain during or after chinning.
Several years ago, I got into doing weighted chins. I kept adding weight week to week to where I was doing 8-10 reps per set for five sets twice a week with 75 lbs at a bodyweight of about 140 lbs. Then I began noticing a pain in my elbow on the first rep of the first set, but nothing after. I ignored it, and in about two weeks it became the first rep of every set, and then shortly after that I noticed it when doing any kind of pulling or curls.
It was tendonitis, and it put me out for 8 months. I saw doctors, they sent me to PTs, they gave me a brace and other nonsense that did nothing to help. I couldn't understand what could be so wrong that months of rest could not solve.
Finally, I saw an athletic trainer, and he explained right away that the bitch of tendonitis is that the inflammation leads to weakening of the muscle, which leads to more strain on the tendon, which in turn creates more inflammation. So when, after resting, you return to training, the tendonitis returns immediately.
The key to beating elbow tendonitis is, after an initial period of rest and icing, to start doing very light forearm exercises to pump blood in the area to promote healing and to gradually strengthen the muscles around the tendon. Rehab is critical.
After that experience, I swore off heavy chins. This past fall, I got back in to doing them again. One month ago, I noticed elbow problems again -- this time on the outside of the other elbow. But it still hurts to grip things; too many weeks of too much heavy pulling and chinning. It was not the chins or the pulls per se, but rather stupidity on my part. Even before I started to feel any pain I knew I should back off for a bit and change my exercises, but I was stubborn. And now I am paying the price.
When I return, I will be doing regular forearm and grip work. Relative to my back in particular, my forearms and grip are weak, and that imbalance has led to this problem. Live and learn, but better to learn from others' mistakes than your own.
Here is a link to a page that explains something about rehabilitation:
Oh, and yes, age makes a difference. Older athletes get tendonitis more often.