This is basically how I would feel in this situation. Nothing would stop me from saving that chicken, and it would get awkward as heck if for some reason we failed.

This is true in pretty much any roleplaying game, up to and including video games.

In Fallout 4, there's a moment in which a kid's cat has gone outside the safety of an underground bunker. There are basically literal monsters outside, so I consider it one of the most important missions in the game to complete.

All it involves is going outside, finding the cat relatively close by, and telling them to go home.

Which works.

I choose to think of it less as the cat obeying your command, and more the cat reacting with "who is this weirdo, I'm going home."

Also, the cat only gets out because the entrance to the bunker was opened to let you in, but I will not be blamed for that cat leaving. That cat was DETERMINED. You can literally close a door in their path, and they'll run into it, glitch into the air as the door opens for them, fall back down, and just keep going until they're outside.

That is all AFTER the cat went up an elevator.

If they hadn't opened the multi-ton mechanical entrance to the bunker to let me in, that cat would've opened it to get out.