Uh, oh! You better not! The Episcopal Church wouldn't mind, but your own church would. The problem involves perceiving communion in an Episcopal church as interchangeable with Catholic Eucharist.
The Episcopal Church's policy is that any baptized Christian can receive Communion in the Episcopal church (and they let their members receive Communion in any church that welcomes them). But for Catholics, the Vatican counts as valid only Catholic Eucharist--bread and wine that have been consecrated by a priest as part of a Catholic Mass. (A few exceptions apply, which are noted in the chart at the right.)
What about Protestants visiting Catholic churches? Restrictions against their receiving Catholic Communion are outlined in the Catholic Catechism, and are invariably in the notes on Communion in the missalettes distributed at Catholic churches. Such restrictions are frequently accompanied with regrets about the lengths which various Christian denominations still must travel to achieve oneness and ecumenism.
Catholicism's lack of an "open table"--the phrase some churches have adopted for sharing the Lord's Supper with those from other Christian denominations--stems from two arenas: Catholics' belief that Communion is the actual presence, through the mystery of transubstantiation, of the blood and body of Christ. This significantly differs from many other Christians' belief that Communion is a remembrance of the sacrificed Christ. The other reason for the restriction is that open Communion would be somewhat dishonest, signaling a church-wide unity that does not yet exist.
What's odd, though, is that Pope John II has occasionally bent his own church's rule so he could provide Communion for certain Protestant leaders and a few non-Catholic ambassadors. Perhaps, in time, there'll be enough "bending" so non-Catholic Christians can bend their knees before a Catholic altar and take Communion.