As a commonly asked question on the Boards, this question was recently addressed by Riot Tantram:
[{quoted}](name=Riot Tantram,realm=NA,application-id=ZGEFLEUQ,discussion-id=MIBGEN1J,comment-id=0005,timestamp=2016-11-04T18:27:06.672+0000)
This is not entirely true. The amount of time it takes to be back in good standing is related to how severe your behavior was, what your last penalty was, how often you've been penalized, and you current behavior. Players who are having a bad day, penalized for behavior that is out of character for them and get a light penalty with be back in good standing rather quickly. Players with a history of poor behavior, those who frequently receieve penalties, and those exhibiting severe behavior will take longer.
The 3 month mark that is repeated on the boards is related to a quote saying it takes the average penalized player 3 months to get back in good standing.
There is no cut and dry answer to how long it'll take before you're eligible for rewards again; however, as the 10-game chat restriction is closer to the bottom of the punishment ladder, if you continue to avoid displaying toxicity as you play, you should become eligible for loot relatively quickly.