Can I keep a hen as a house pet?

You can if you are not too fussy about mess on the furniture, but it might be
healthier for the hen to live out of doors and just come in occasionally as a
visitor. I once saw a house hen brought in for hospital treatment at The Blue
Cross animal hospital in London. Her owner was insisting that she should have
tea (with one sugar) and a biscuit in the mornings.
Another house hen was Hatty who slept in the kitchen at the end of a 120cm piece
of furniture. Felix, the cat, slept at the other end. He, and the dog would watch
her war dance with anxious eyes. Her owner reported: "Hatty stands and eyes
them up and down in a way that leaves them no doubt as to their expected behaviour
- and they obey. Felix takes the same line of least resistance as the dog, and
the result is a happy family. Only one animal does not kowtow and
that is our tortoise. Hatty used to stand on its carapace and issue orders but
all that happened was that she was thrown off by the lurch as the tortoise got
under way."
If you want to reduce hen muck on the furniture, you could let the hens into the
house during the day but keep them in a hen house at night. Quite a few outside
hens visit their owner's kitchens (no guesses why) during the day time! A bantam
used to visit her owner's house and lay her egg on a wire dish tray on the draining
board!
Bade, a Rhode island red named after a Salvation Army Lt Col, came in to join
the family in the conservatory after she had mastered the cat flap. She asserted
her authority over the cats early on in their relationship! "She is very
blasé about the cats and is not averse to giving them a peck," reported
her owner.