For the first time I have seen hen eggs with two yolks.
Do they indicate a special kind of hen?
OR A special kind of grain fed to the hen?
OR Some scientific procedure which makes hens produce such eggs?
Are these kind of eggs safe to eat?
Double-yolked eggs are the result of an anomaly in the egg generation process in the hen.
They can happen in any breed of hen, on any feed. It is a result of two ova being generated at the same time, and then encapsulated in a single shell. According to My Pet Chicken, it happens more often with younger hens.
I am not aware of any process to intentionally foster double yolked eggs, but that doesn't mean such a thing doesn't exist.
They are safe to eat, although they may be visually startling.
A hen aged between 20-28 weeks has a one in a hundred chance of laying a double yoked egg. Since all the eggs in a box usually come from the same flock and all the birds in the flock are the same age, if you find one double yolk, the probablity of finding more in the box is high. As double-yoked eggs are larger than single yoked, if the eggs are graded to be the same size in a box, the probability of finding them increases.
According to my onetime teacher in Reproductive Biology at Oregon State University (Go Beavers!), Fred Menino, hens commonly lay multiple yolk eggs (I think the record is 9 yolks, but I may be mis-remembering) when young, before they are completely reproductively competent. To some degree this is a result of the selective breeding programs we (humans) have used to increase the numbers of eggs chickens lay in their most productive laying years, which favors hens that reproduce early in life.
So, to answer the question(s): Yes, it is a special sort of hen, bred for generations to lay huge numbers of eggs. It is not a special kind of grain; though the diets of commercial layers is very carefully chosen to maximize egg-laying, that just means getting the hens the closest to perfect nutrition for making lots of eggs. The scientific procedure is selective breeding for maximum egg-laying. This is very powerful. It's not "genetic engineering", but has results very quickly, and has been practiced since humans have been breeding animals for food and profit.
The eggs are as safe as any other egg.