Is It Permissible to Donate Human Eggs?

I assume you are referring to a woman donating her egg cells (also called ova) for reproductive purposes and not to someone donating the kind of eggs you buy at a grocery store to someone who is hungry. The answer is that human egg cells may not be donated for reproductive purposes. The Catechism of the Catholic Church states:

Techniques that entail the dissociation of husband and wife, by the intrusion of a person other than the couple (donation of sperm or ovum, surrogate uterus), are gravely immoral. These techniques (heterologous artificial insemination and fertilization) infringe the child’s right to be born of a father and mother known to him and bound to each other by marriage. They betray the spouses’ “right to become a father and a mother only through each other” (CCC 2376).