Found in deathclaw nests. Sometimes the eggs will appear placed on top of the nest as well as lootable from in the nest itself, allowing the collection of more than one at a time. There are several deathclaw nests across the Commonwealth including:
North of Fort Hagen filling station, in a small pond area with a white pickup truck in the pond. The cave is near a fridge sunken into the ground.
Northwest of the Mass Pike Interchange's elevator, beneath a rocky overhang. Mist rises from the ground, and a deathclaw guards the nest. This location appears to be a permanent nest, given the corpses around that cannot be interacted with, and its contents respawn (often along with the deathclaw)(same location as above).
On Far Harbor Island, west of the Vim! Pop factory under a rocky overhang. There is a tent to the south. There are two nests in this location in one pile, for double the spoils. It is guarded by a leveled deathclaw.
Other nests are rarely encountered in any location that is a random creature spawn, and are often guarded by a powerful enemy such as a deathclaw, or a yao guai. There is no minimum level for these to spawn in, and may be the cause for random deathclaw encounters in the Commonwealth where formerly there was not one before.
This article is too short to provide more than rudimentary information about the subject. You can help Nukapedia by expanding it.