Do you mean the inside ring at the pedal crank or the small cog at the wheel?  Any shop can adjust you pretty cheap, but if you are a diyer there are high and low limit screws on both the front and rear derailleurs. If it's at the crank, tighten the low limit screw 1/4 to 1/2 turn on the front derailleyr until it stops falling off. If it's at the rear wheel, do the same for the high limit screw on the rear derailleur.

Dirkdee wrote on 10/07/14 at 4:24pm:


chains slap against frames all the time.  that's why they sell so many chain-stay protectors.  It's not as likely that he has too many links in his chain as it is, his limit screws need some adjustment.  I"m not sure I agree with the worn out derailleur idea nor the narrow wide chain ring idea.  I would assume is running multiple rings up front.  As a beginner rider, that's probably a better choice than a 1x setup until he knows how to ride.

Before screwing with the limit screws, try adjusting the cable with the knob on the shifter. You may need to shorten the cable. Go easy 1/2 turn at a time.