When I was a kid (born in 1979), I remember my family watching a show or movie about a large statue of an egg. The egg was being studied by someone, possibly a journalist, who took pictures of the egg regularly until it finally hatched a demon or gargoyle of some sort. I also remember it flying and chasing a man while beams shot out of its eyes. Was this real? Does anyone else remember this?
I think you are looking for Witches Brew (1980)
And on IMDB.
As part of the plot:
Meanwhile, Vivian Cross (Lana Turner) is controlling several of the other wives via a sculpture of an egg (modeled on a demonic witches' egg they find in a book on witchcraft) in which a being is hatched. This winged creatures whose eyes shoot green flames chases Joshua's car and nearly kills him before Vivian destroys it via her magic.
You can see the whole film here. The bit with the egg and the laser-shooting gargoyle starts at around the 50 minute mark.