The reading is from Acts of the Apostles 1:12-17, 21-26

In those days, the apostles returned to Jerusalem from the mount called Olivet, which is near Jerusalem, a sabbath day's journey away; and when they had entered, they went up to the upper room, where they were staying, Peter and John and James and Andrew, Philip and Thomas, Bartholomew and Matthew, James the son of Alphaios and Simon the Zealot and Judas the son of James. All these with one accord devoted themselves to prayer, together with the women and Mary the mother of Jesus, and with his brothers.

In those days Peter stood up among the brethren (the company of persons was in all about a hundred and twenty), and said, "Brethren, the scripture had to be fulfilled, which the Holy Spirit spoke beforehand by the mouth of David, concerning Judas who was guide to those who arrested Jesus. For he was numbered among us, and was allotted his share in this ministry. "So one of the men who have accompanied us during all the time that the Lord Jesus went in and out among us, beginning from the baptism of John until the day when he was taken up from us -- one of these men must become with us a witness to his resurrection."

And they put forward two, Joseph called Barsabbas, who was surnamed Justos, and Matthias. And they prayed and said, "Lord, who knowest the hearts of all men, show which one of these two thou hast chosen to take the place in this ministry and apostleship from which Judas turned aside, to go to his own place." And they cast lots for them, and the lot fell on Matthias; and he was enrolled with the eleven apostles.