The answer
If there is another priest in the church, then he is the one who should help with the Communion, and the deacon, in this situation, is not allowed to take the chalice since there is no pressing need for him to do so.
But if there is only one priest, then there exists a basic condition in which the deacon could perform this task and is permitted to do so, if in the circumstances the serving priest is unable to give Communion to all the people. This condition stipulates that:
The deacon should be wholly consecrated in order to be able to assist the priest, by virtue of his rank, and to be
completely devoted to the Church's ministry, and wear clerical dress.
He must be someone who doesn't have an ordinary job, or wear ordinary clothes outside the church, and he must be recognisable to the people as someone who has consecrated himself to the religious ministry. According to Church rules any bishop, priest or wholly consecrated deacon who involves himself in an outside job (that is, works outside the Church) should be cut off.
If the wholly consecrated deacon takes the chalice in a situation where there isn't another participating priest then he will not be offending the people at all.
It is not permitted, however, for deacons of any lesser rank to do so. This is because serving at the altar and receiving the holy sacraments, is not something everyone can do, but is only for those who have devoted themselves to the ministry, and each one should only undertake the duties appropriate to his rank.
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Thrice-Blessed Pope Shenouda III of Blessed Memory