After a few months she agreed to meet her new friend.
The Home Office is warning that up to one in five children could be in danger from these internet abusers.
In an unpublished report obtained by the BBC, the Home Office said those most at risk are girls aged 13 to 17.
BBC correspondent James Westhead spoke to 13-year-old Georgie about a frightening experience which began when she met someone on the internet.
She thought the friend she was meeting every night on the internet was a 15-year-old boy.
"As the relationship developed we started talking on the phone, ringing each other every night for hours," said Georgie.
After a few months she agreed to meet her new friend.
Luckily, her mother Katherine insisted on going with her and was horrified to see her daughter's new friend was a 47-year-old man.
He was arrested but under UK law no crime had been committed.
In a separate case last October, 33-year-old Patrick Green was jailed for five years after pleading guilty to sexually abusing a 13-year-old girl he met through an internet chatroom.
Nigel Williams of children's charity ChildNet International thinks police should be able to step in before such abuse takes place.
"Police should be able to intervene and arrest people before they harm children, because they see them enticing children and attempting to lure them to a meeting where they can sexually assault them," he said.
Last October, his charity set up a website to warn children of the dangers of chatrooms.
The Home Office report Chatroom Danger identifies three other areas of concern:
Home Office minister Lord Bassam said a review of the law was being considered.
"As a parent I am extremely concerned about these issues."
He said internet crimes would be tackled by a new high-tech crime group to be set up in April.
But shadow home secretary Ann Widdecombe said: "Over the past nine months, Conservative attempts to change the law in this area have been rejected six times by the government.
"If a Home Office report has called for a change in the law, then [ministers] will have a lot of explaining to do."