The chat took place in the Santa MartaÂ residence, the guest house in Vatican City where the pontiffÂ lives.
Zuckerberg wore a dark suit and tie for the occasion while Ms Chan wore aÂ black, knee-length dress.
The 32-year-old tech billionaireÂ said on his Facebook page it was an honour to meet the pontiff.
He added: â€œIt was a meeting weâ€™ll never forget. You can feel his warmth and kindness, and how deeply he cares about helping people.â€
Vatican spokesman Greg Burke said they discussed â€œhow to use communication technologies toÂ alleviate poverty, encourage a culture of encounter, and make a message of hopeÂ arrive, especially to those most in needâ€.
Also on Monday, ZuckerbergÂ met Prime Minister Matteo Renzi and went for a jog around the Colosseum.
He discussed with the Italian premierÂ last weekâ€™s earthquake, and how the Facebook community hadÂ helped.
Zuckerberg is in Italy for a conference at Romeâ€™s Luiss university.
He and his wifeÂ spent their 2012Â honeymoon in the Eternal City, flying there by private jet and staying in a luxury hotel near the Spanish Steps.