EWTN Catholic Q&A
Question from anon on 06-14-2011:

Are Roman Catholics allowed to receive communion in the Eastern Catholic Churches?

Answer by Colin B. Donovan, STL on 07-05-2011:

Canon 923 states: The Christian faithful may take part in the Eucharistic Sacrifice and receive Communion in any Catholic rite.

This means that one can also fulfill the Sunday obligation by participating in the Eucharist offered in any Catholic Rite (Roman Rite, whether Ordinary or Extraordinary Form, Ambrosian, Ukranian, Maronite, Melkite, Ruthenian, Syro-Malabar, Chaldee etc.).

So if there are Eastern Churches in communion with Rome in your town you are free to participate in the Divine Liturgy (Holy Mass) and learn more about the treasures of Christ's Church.