The 27-year-old bit the Juventus defender during the South American side’s crucial Group D encounter at the Arena das Dunas in Natal on Tuesday.
The incident occurred in the 79th minute when the former Ajax star dug his teeth into Chiellini without being provoked.
It was the third time in his career that Suarez had bit someone on the football pitch and has been severely punished by FIFA.
Suarez has been suspended for nine international matches and has been given a four-month ban from all football-related activities by FIFA.
The former Ajax star was sent home from the World Cup, as Uruguay lost to Colombia in the last 16.
Suarez has now publicly apologised for his actions and has promised that he will not commit the same offence again.
The former Nacional star posted the following message on social networking site Twitter.
Should this make Liverpool fans relieved? Probably. After all, Suarez seems to be accepting his fault and publicly saying that he will not bite anyone again.
Since FIFA announced the punishment, Suarez got support from his Uruguay teammates and his friends, and there was a feeling that he was not ready to accept responsibility for his actions.
However, Suarez’s latest comments do suggest that he genuinely regrets what he did and is determined not to do it again.