Looks to me like they do,P. In the Eastern Churches a different discipline has been in force for many centuries: while bishops are chosen solely from among celibates, married men can be ordained as deacons and priests. This practice has long been considered legitimate; these priests exercise a fruitful ministry within their communities. Moreover, priestly celibacy is held in great honor in the Eastern Churches and many priests have freely chosen it for the sake of the Kingdom of God. In the East as in the West a man who has already received the sacrament of Holy Orders can no longer marry. (CCC 1579-1580)
“Looks to me like they do,”
So much for your eyes then.
http://www.vatican.va/archive/ENG0015/__P4X.HTM
1579 All the ordained ministers of the Latin Church, with the exception of permanent deacons, are normally chosen from among men of faith who live a celibate life and who intend to remain celibate "for the sake of the kingdom of heaven."70 Called to consecrate themselves with undivided heart to the Lord and to "the affairs of the Lord,"71 they give themselves entirely to God and to men. Celibacy is a sign of this new life to the service of which the Church's minister is consecrated; accepted with a joyous heart celibacy radiantly proclaims the Reign of God.72
1580 In the Eastern Churches a different discipline has been in force for many centuries: while bishops are chosen solely from among celibates, married men can be ordained as deacons and priests. This practice has long been considered legitimate; these priests exercise a fruitful ministry within their communities.73 Moreover, priestly celibacy is held in great honor in the Eastern Churches and many priests have freely chosen it for the sake of the Kingdom of God. In the East as in the West a man who has already received the sacrament of Holy Orders can no longer marry.