Can a Christian observe the Lord's supper (i.e., communion) alone?
The most specific instructions in Scripture concerning the way the Church should observe the communion meal is found in Paul's teaching in 1Corinthians 11.
In this passage, Paul clearly expected the Church to observe this communion meal in the context of a gathering. Paul's instructions include statements like "...when you come together as a Church..." and "...when you meet together..." which strongly suggests Paul expected the meal to be conducted in a corporate setting.
Furthermore, the original Last Supper observance by Christ was based on the Passover celebration, which was required to be conducted in a group setting:
Notice that smaller families were required to join together with to form larger groups that would ensure the lamb was fully consumed. Therefore, it was not possible for a Jew to observe the Passover meal alone. Here again, this pattern argues against an individual observance of the Lord's Supper, since it is modeled after the Passover. (For more background on the connection between Passover the and Lord's Supper, please listen to Lesson 13 of our John's study.)
Finally, observing the Lord’s Supper individually is not necessary. The purpose of the observation, according to Paul, is to witness to the sacrifice of Jesus and His promise to return for the Church (see 1Cor 11:26). By definition, we cannot offer a witness without an audience, so communion's chief purpose according to Paul cannot be achieved when we're alone.
For all these reasons, we do not believe a Christian should attempt to conduct communion alone. Doing so is likely nothing more than eating a meal.