Catholics and Eastern Orthodox Communion
Does the Eastern Orthodox Church allow Catholics to receive the Eucharist?
The answer is no. Although there might be individual Orthodox clergy who would give you as a Catholic Communion, it still remains true that there is no Orthodox church that permits Catholics to receive Holy Communion at their liturgies. Even so, if you happen to be at an Orthodox liturgy on a Sunday or holy day, this does fulfill your obligation, even if you are not able to receive Holy Communion.
The reason is that the Orthodox have a genuine priesthood and so a genuine Eucharist. The Orthodox are generally admirable in their reverence for the reception of the Blessed Sacrament, which they receive following the ancient discipline of fasting and confession of sin. Married Orthodox priests and laity who follow the canons of their church even abstain from marital relations before communing. Thus there is another reason not to present yourself for Holy Communion at an Orthodox liturgy: you are probably not observing as a Catholic their discipline of preparation for the reception of the sacrament.