The offence happened on Regent Road car park in Altrincham and she received a fixed penalty of£50.
Executive councillor June Reilly said:
'Chewing gum is very expensive to clear off the streets and six out of ten Trafford people put litter as their top environmental priority in our Street Pride research last year.
'We are responding to their views by using the new fixed penalty powers where necessary and urge people to act responsibly by disposing of chewing gum properly.'
Since January 783 people have received fixed penalty notices for a range of littering offences.
It is now an offence to drop, throw, leave or deposit litter (including cigarette butts and chewing gum) in a public place.