Before the Great Schism, there was Chalcedon

In the year of the Lord 451, the Council of Chalcedon was convened.

From Wikipedia:

The Council of Chalcedon was an ecumenical council that took place from October 8–November 1, 451 at Chalcedon, a city of Bithynia in Asia Minor. It is the fourth of the first seven Ecumenical Councils in Christianity, and is therefore recognized as infallible in its dogmatic definitions by the Roman Catholic and Eastern Orthodox churches. It repudiated the Eutychian doctrine of monophysitism, and set forth the Chalcedonian Creed, which describes the full humanity and full divinity of Jesus, the second person of the Holy Trinity.
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The near-immediate result of the council was a major schism. The bishops that were uneasy with the language of Pope Leo's Tome repudiated the council, saying that the acceptance of two physes was tantamount to Nestorianism. This is the origin of Oriental Orthodoxy, which still today rejects the results of this council.

Fast-forward 1555 years to the present.

Pope Voices Desire to Mend a 1,500-Year Split

Promotes Unity With Armenian Apostolic Church

VATICAN CITY, MARCH 20, 2006 (Zenit.org).- Benedict XVI signals his desire to promote unity with the Armenian Apostolic Church, a Christian confession that separated from Rome in the fifth century.

The Pope expressed his desire for unity today when he received in audience His Beatitude Nerses Bedros XIX Tarmouni, Catholic patriarch of Cilicia of the Armenians, Lebanon, with members of the patriarchal synod and a group of pilgrims.

The Mideast-based patriarch leads 600,000 Catholic faithful in communion with Rome, assisted by 120 priests and about 90 women religious, according to Vatican Radio.

By contrast, more than 90% of the Armenian Christians are under the Armenian Apostolic Patriarchate, which separated from Rome after the Council of Chalcedon in 451. A key step toward overcoming this division was taken in 1996 when Pope John Paul II and Patriarch Karekin I signed a joint declaration on the nature of Jesus. [...]

Everyone, everyone (!) gets a seat on the Benedict Bus to Greater Communion. It is of course to be expected. As CWN points out in its own article, John Paul II and the late head of the Armenian Church signed a joint statement "essentially ending the doctrinal disputes that caused a split after the Council of Chalcedon in 451."

The question then of course becomes just how one brings the two churches together. Would the Armenian Church unite with its Eastern Rite cousins? Would it become an entirely separate Eastern Rite? Such questions will need to be answered.