JOEL - I have not heard of any specific position that the Church has taken on egg donations. But according to the General Handbook of instructions;

"In vitro fertilization using semen from anyone but the husband or an egg from anyone but the wife is strongly discouraged. However, this is a personal matter that ultimately must be left to the judgment of the husband and wife, with responsibility for the decision resting solely upon them."(page 158)
"The donation of sperm is strongly discouraged."(page 158)
"Surrogate motherhood is strongly discouraged"(page 159)

If using an egg from anyone but the wife is discouraged, then logic would suggest that donating an egg to someone else would also be discouraged. Of course, I don't think anyone is going to lose their church membership if they decide to donate eggs. As with many other such things it is up to the individual to talk it over with their Bishop and make a prayerful decision about what is the right thing to do.