What is a golden egg? Do they kill the hen that lays them ?English only!?

Sounds like the golden comb of Solomon bird.

The Goose That Laid the Golden Eggs is one of many fables attributed to Aesop, and one that can be found in a compilation of his works cited and sourced at the bottom of this article. It is very popular, as are many of his fables, which also include The Fox and the Grapes, The Boy Who Cried Wolf, and The Tortoise and the Hare.

A man and his wife had the good fortune to possess a goose which laid a golden egg every day. Lucky though they were, they soon began to think they were not getting rich fast enough, and, imagining the bird must be made of gold inside, they decided to kill it in order to secure the whole store of precious metal at once. But when they cut it open they found it was just like any other goose. Thus,they neither got rich all at once, as they had hoped, nor enjoyed any longer the daily addition to their wealth.

so yup they did kill it