Should the Eucharist be celebrated alone or with a congregation? This question has been argued vehemently by each side. Obviously, most would argue clearly that it is better to have a congregation. In my most humble opinion, it does not prevent us from celebrating the sacrament when alone. I arrived at this decision some time ago when I viewed the movie "When in Rome." It is a movie with Van Johnson about the 1950 Holy Year and is, sadly, not yet released on DVD.
The plot of the movie is that a convict boards a boat with a priest and then steals his identity to escape unnoticed in Rome during the Holy Year. Obviously, there would have been a gaggle of priests in the Eternal City. The criminal eventually finds himself in a Trappist-style monastery and the priest, Van Johnson, says something like "there is great consolation knowing that you are here praying for me and the entire world." I'm paraphrasing, but this is a crude comparison to my own Eucharistic beliefs.
The Eucharist is a means of grace to us, but there is also a sort of metaphysical grace that is conferred on the greater world when the Eucharist is celebrated. It is the recognition of Christ's presence among us in a more tangible way with his very Body and Blood. It is good when this is done either alone or in community. There have been times of great spiritual difficulty that I have celebrated the Eucharist alone and received the graces conveyed very tangibly.
What does this mean in the greater theological schema? Does it necessarily convey that we, as priests, are custodians of the sacramental power without the need to offer sacrifice on behalf of the greater community? Well, no. But, in solitary eucharists we do offer sacrifice on behalf of the very world even, as the old saying goes, if we are only surrounded by the saints and angels. Now, we even have the ability to broadcast our liturgies across the world. I know several priests who have successful apostolates broadcasting their masses to those who cannot attend elsewhere.
Is this the only ministry for which a priest can be ordained? Well, not necessarily. Unless one is a true hermit or some other type of recluse, there is still a commitment to minister to the People of God. We exist to serve them and to bring Christ to them in the graces of the sacraments. This looks vastly different to each person--how they absolve others and spread the Gospel. It is also not limited to space--I know priests who have ministered more in grocery stores, parking lots, among friends, and in other places than they do in a "traditional parish." Perhaps that is more close to the message of Jesus than we think.
"And into whatsoever city ye enter, and they receive you, eat such things as are set before you: and heal the sick that are therein, and say unto them, The kingdom of God is come nigh unto you." Luke 10: 8.