For Orthodox Christians, the Eucharist is a visible sign of unity; to receive the Eucharist in a community to which one does not belong is improper. If one does not accept all that the Church believes and teaches and worships, one cannot make a visible sign of unity with it. The Eucharist is the result of unity, not the means by which unity is achieved. While many non-Orthodox see this as a sign that the Orthodox Church excludes non-Orthodox from the Eucharist, in reality the opposite is true. Because a non-Orthodox individual has chosen not to embrace all that Orthodox Christianity holds, the non-Orthodox individual makes it impossible for an Orthodox priest to offer him or her communion. It is not so much a matter of Orthodoxy excluding non-Orthodox as it is the non-Orthodox making it impossible for the Orthodox to offer the Eucharist.
From the OCA website, which I neglected to include in my above post...