Every year since 1908, beginning on January 18 and ending on the Feast of the Conversion of St. Paul on January 25, the Graymoor Institute and the Franciscan Friars of the Atonement have been promoting a focused week of prayer and reflection, asking God to bring unity to the body of Christ.
The idea of an octave of prayer for unity among Christians was the brainchild of Servant of God Fr. Paul Wattson, who conceived of it while he was still an Anglican. In a 2016 lecture at St. Paul Seminary School of Divinity in Minnesota, Msgr. Jeffrey Steenson gave a thorough and fascinating presentation on the man behind the International Week of Prayer for Christian Unity, which you can watch here: