I've had a few of them get killed by Giants. Lydia always replaces them when I ask her to, but now the dialogue option isn't there. She'll still offer to buy a Horse or Cow, but no Chicken.

The little bugger isn't in her pen, and I can't find her anywhere around Lakeview Manor. Is there a glitch where it wanders off or something? I'm assuming she's still alive since I don't have the option to buy another one.