Kill the "chicken"

 is an unmarked quest in Fallout 2.

Walkthrough
The "chicken" that Rose gets her Wasteland Omelettes from is actually a very fearsome deathclaw!

You can kill it for 1000 (800) XP and a drop in Modoc town reputation. Rose will also no longer sell the Omelettes. Killig Rose's deatchclaw while sneaking and without being detected will not result in a Modoc reputation drop. Upon asking for an omelet, Rose will simply tell the player that she no longer offers them because "some fool broke into our coop and killed our ... chicken".

This quest is mentioned in Fallout: New Vegas by Jas Wilkins, Rose's great-niece, who offers the Courier the recipe whilst recalling the story of someone coming to town and shooting the Deathclaw "right in the eye".