Cox, who is best known for her role as Monica Geller in the US sitcom, was in the Capital supporting her Snow Patrol star boyfriend, Johnny McDaid, who is playing a gig at the venue tonight.
And Fraser Ogilvie, who drives a black cab in Edinburgh, was given a surprise when the actress jumped into his car on Tuesday night.
Speaking to the Daily Record, Fraser said he even refused money for the ride in exchange for a picture with the A-lister.
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He told the newspaper that his wife is a huge Friends fan too and "would have killed me if I never got a photo."
Fraser uploaded a picture of the pair on social media and joked: "Just a friend in the taxi #NaeTip."