Officially, yes – Christianity is one of three religious minorities recognized by the Iranian government (the other two are Judaism and Zoroastrianism.) The Islamic Republic of Iran is officially a theocracy, in which political and religious authority are intertwined. Shia Islam is the state religion, but these three groups – which together make up barely 2% of the population – are protected and enjoy certain rights, such reserved seats in parliament. The majority of Christians in Iran are members of the Armenian Catholic Church or the Chaldean Catholic Church, both of which are in communion with Rome. Christians are viewed as ethnic minorities and must celebrate their liturgical rites in Armenian or Chaldean, not in Farsi, the common tongue.
However, day-to day life can be extremely difficult for Christians. Conversion from Islam to another religion is forbidden in Iran and punishable by death; non-Muslims face more severe punishments for crimes than Muslims. Because Iran is a theocracy, any public expression of a religion other than Islam can potentially be interpreted as political opposition and thus is subject to repression. In most cases the directors of Christian schools are Muslims, as required by law. And Christians cannot hold high government positions and often face difficulty finding jobs at all. Emigration from Iran since the 1979 Islamic Revolution has decimated its population of Christians, and some commentators even speak of the impending extinction of Christianity in the country.