You cannot outrun these so you must use stealth. When near the nest you must crawl around and use objects to hide yourself from the full grown ones. Secure the egg and get the hell out of there and make sure to run away by running behind objects so it slows them down.
I was sitting on a flyer on a cliff above the deinos, thought I was safe to wait for my moment to steal their eggs...had the biggest heart attack when one of them decided to climb up the cliff. I accidentally dismounted in shock and fell right into the packs claws, where they shredded me to death. Don't be scared of them, they smell it.
The guy that said that they can be found in places other than chalk hills and at “green spire.” It took me like a half an hour of research to find what you were talking about. It’s not called a “spire” it’s an obelisk.