Sadly, Mammoths Didn't Lay Eggs

But the moa and Aepyornis did. An article in BBC says, "Researchers have found that eggshells of extinct bird species are a rich source of preserved DNA." I hadn't realized just how recently these giant flighless birds had gone extinct:

The elephant bird may be at the root of legends about giant birds. Marco Polo claimed erroneously that these giant birds could fly. There are also tales of birds that could pick up elephants in 1001 Arabian Nights.

It's no Jurassic Park or anything, but a person can dream, right? I'll be the one looking for mammoth eggs.

Followup: The Guardian also has an article, with more info, and a clearer description of the birds in question. And a squeee cute photo of an emu hatchling.