In the thirteenth century a Chinese Christian belonging to the Church of the East decided to go on a pilgrimage to the Holy Land. His name was Rabban Bar Sauma, and he was born in Beijing and became a Christian priest. He set out on the pilgrimage with a student of his, named Rabban Markos, and they got as far as Persia, where they met with the Catholicos (patriarch) of the Church of the East, who was Mar Denha I. In the course of their travels they learned that the entire region around the Holy Land was in a state of tumult and war, so while they were wondering what to do, the Catholicos asked them to go to the court of Abaqa Khan, to get the documents officially recognizing Mar Denha as the patriarch. They did this, and Mar Denha intended to send them as messengers to China, but war to the east prevented that as well, so they stayed in Baghdad making themselves useful for a while. Mar Denha then died, and Rabban Markos was elected Catholicos of the Church of the East, taking the name Mar Yahballaha III. They went to Abaqa again to get the official confirmation letters, but Abaqa had died and his son Arghun had become ruler of the Ilkhanate.
The Mameluk territories to the south and west were extreme irritations to Ilkhanate, and so Arghun Khan hoped for an alliance between the Buddhist Mongols in the East and the Christian Franks in the West to fight together and conquer the Muslim Mamelukes Syria and the surrounding region. He asked Mar Yahballaha to recommend someone to go to the West with letters proposing it. Mar Yahballaha, of course, recommended his teacher Rabban Bar Sauma. So Rabban Bar Sauma, who had never been able to complete his pilgrimage to Jerusalem because of the dangers, in his old age now had a new pilgrimage.
It was quite a journey. He visited Constantinople and was stunned by Hagia Sophia; while there he met with Emperor Andronikos II Palaiologos. He sailed to Italy, and as they were sailing past Sicily, he saw the eruption of Mount Etna on June 18, 1287. On June 24, 1287, he saw from a distance the Battle of Sorento, a naval battle between France and Spain in the War of the Sicilian Vespers.
A big part of Bar Sauma's mission was to deliver the messages to Mar Papa, the Catholicos of the West, but when he got to Rome, the pope had recently died. So he toured St. Peter's and talked with Cardinals. Since they were thirteenth-century Catholic churchmen, they wanted to discuss and argue, and so they asked Bar Sauma what his views on various theological topics were, and he acquitted himself fairly well, although he had to cut them short and finally tell them that he wasn't there to debate theology to deliver his letters and received the blessing of the Mar Papa in Rome. Since there was no Mar Papa at the time, he continued on his way: Tuscany and Genoa, where he spent the winter, and then on to France, where he met King Philip the Fair. King Philip was interested in the alliance, and so arranged to have a French nobleman go back with Bar Sauma whenever he ended up going back. In Gascony he delivered the message to King Edward I of England, as well, who would eventually send an ambassador to Arghun Khan's court. (Despite the interest, however, very little ever came of the attempt to build a Franco-Mongol Alliance.)
Bar Sauma was a bit worried about not having delivered a message to Mar Papa -- it meant his mission was strictly speaking a failure, and Mongol governments were not exactly tolerant of failure. One of the people Bar Sauma had talked to, however, had business that took him to Rome, and so Bar Sauma received a message from the newly elected Mar Papa, Pope Nicholas IV, inviting him to Rome. So back to Rome he went to meet with the Pope and deliver his message; the Pope asked him to stay for the holy days, because it was halfway through Lent. He was treated with great hospitality, and he suggested to the Pope that he should celebrate the Divine Liturgy one day so that the Pope would know what the Use of the Church of the East was. The Pope thought this was an excellent idea, so Bar Sauma celebrated the Divine Liturgy to a very large crowd who were curious to see how Christians among the Mongols said Mass. The people were impressed, and said that it was the same rite as their own, just with differences you'd expect from the differences in language.
So Bar Sauma asked for something a bit more courageous: he asked if he could receive communion from the Pope himself. And on Palm Sunday, he did. It was a very emotional experience for him. He saw the service of Holy Thursday in St. John Lateran, and the Maundy footwashing, the Good Friday procession, Holy Saturday and the Easter Vigil, and then Easter Day at St. Mary Major, and a week later a consecration of bishops.
The Pope invited him to continue to stay in Rome, but Bar Sauma had to get back to let people know that he had finished his mission. He asked the Pope for relics to take back with him. The Pope pointed out that they couldn't give relics to everyone who came to Rome, or they'd soon have none, but because Bar Sauma's pilgrimage had been so unusually long, they would make an exception in this case, so they gave him some small relics. The Pope also sent with him a tiara and vestments for Mar Yahballaha and a papal bull recognizing Mar Yahballaha's authority and jurisdiction as Patriarch over the Church of the East, and naming Bar Sauma as Apostolic Visitor to the East. And so Bar Sauma returned to Baghdad in honor, where he would die in 1294.
But not before he wrote a book describing his extraordinary journey. The original Persian text doesn't seem to have survived, but a Syriac abridgement was made at some point, continuing the story through the entire reign of Mar Yahballaha. The text was completely translated into English in 1928 by Sir E. A. Wallis Budge, under the title, The Monks of Kublai Khan, Emperor of China, which you can read online.
Rabban Bar Sauma's visit may have piqued Pope Nicholas IV's interest in the East; not long afterward he sent several missions to various parts of the East. The most successful of these was that of John of Montecorvino, who founded a Catholic mission in Beijing that lasted for several decades. Mar Yahballaha, in turn, explicitly affirmed communion with Rome in a 1304 letter to Pope Benedict XI; but it was not a union that had much practical effect, or that lasted past his death.