Gomez was jeered by the home support during England's 7-0 win over Montenegro on Thursday.
It came after the Liverpool defender was involved in a bust-up with Raheem Sterling in the canteen at St. George's Park on Monday - an incident that resulted in coach Gareth Southgate axing the Manchester City forward from the squad for Thursday night's win.
"I have known Joe for a long time and it is not nice to hear that sort of thing," Chilwell said.
"No one deserves to get booed, everyone is behind Joe he is a great player and a great guy and we all support everyone.
"I just want and everyone wants the fans to get behind the whole team. We are going to support Joe and Joe is a very strong character.
"He played well when he came on and we are all behind him. Joe is a strong character. He has been great this week in training. His normal self. We all moved on from it the day after it happened.
"We are going to be supportive of him and behind him.
"Everyone has moved on from it in the camp. We just want everyone else, the fans, to move on from it as well."