Suarez - who has actually gone Mike Tyson on opponents on two previous occasions in his career - was not punished by Mexican referee Marco Rodriguez, despite Chiellini's protests.
The Italian even lowered his jersey to show everyone the bite mark on his shoulder.
Just moments after this incident, Uruguay took the lead on a Diego Godin header and went on to win 1-0, qualifying for the round of 16.
Italy, meanwhile, was sent packing as a result of the loss.
FIFA regulations do allow Suarez to be punished retrospectively and it has said it "will gather all the necessary elements in order to evaluate the matter."
Under-fire Luis Suarez has defended accusations he bit an Italian player in a World Cup match - declaring: "These things happen on the pitch."
Suarez spoke out as Fifa announced it is investigating the matter and could choose to suspend the player at least until the end of the tournament.
Defending the alleged attack he said: "These situations happen on the pitch, we were both just inside the area, he struck me in the chest with his shoulder and he hit me in the eye as well.
"These are things that happen on the pitch and you shouldn't attach so much importance to them.
"I'm very happy to have qualified. We are taking each game as it comes, we know that we're in a difficult situation, we're at our limits now."
A Fifa spokesman said: "We are awaiting the official match reports and will gather all the necessary elements in order to evaluate the matter."
World football's governing body can hit players with retrospective bans of up to two years if its disciplinary commission decides there is a case to answer.
The following video makes this abhorrent action rather obvious:
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