Skeptic says:

Source: Catholic Encyclopedia
http://newadvent.org/cathen/05224d.htm

“Because the use of eggs was forbidden during Lent, they were brought to the table on Easter Day, coloured red to symbolize the Easter joy. This custom is found not only in the Latin but also in the Oriental Churches. The symbolic meaning of a new creation of mankind by Jesus risen from the dead was probably an invention of later times. The custom may have its origin in paganism, for a great many pagan customs, celebrating the return of spring, gravitated to Easter. The egg is the emblem of the germinating life of early spring. Easter eggs, the children are told, come from Rome with the bells which on Thursday go to Rome and return Saturday morning. The sponsors in some countries give Easter eggs to their god-children. Coloured eggs are used by children at Easter in a sort of game which consists in testing the strength of the shells (Kraus, Real-Encyklopædie, s.v. Ei). Both coloured and uncoloured eggs are used in some parts of the United States for this game, known as “egg-picking”. Another practice is the “egg-rolling” by children on Easter Monday on the lawn of the White House in Washington.”