Okay, not so much chaos as disorder.
We recently moved down one flight of stairs and 50 feet over. Why would we do this to ourselves? We wanted a larger apartment, but didn't want to lose our location. So when an apartment opened up in the building, we jumped at the opportunity.
The great thing was that we didn't need to pack much. Most of our stuff could simply be carried down the stairs with no boxes required. And I say simply, of course, because I wasn't involved in moving the bed or larger items. I've since heard my husband muttering darkly about how we're going to hire movers next time.
The cat was moved downstairs after the large items, but ahead of the small ones. Predictably, she was highly unimpressed. She wandered around the new apartment meowing plaintively while she explored, checking over her shoulder to make sure I was still there to protect her from any roving creatures that might take a fancy to a cat sandwich. She's since settled down and actually seems to like the new apartment better (which is no doubt helped by a complete lack of menacing creatures who eat cats).
Since we carried everything down without much packing, the chaos with this move was mitigated to disorder. We still have boxes everywhere in the living room, but there are whole patches of clear floor we can walk on. And once we get new book shelves, it should all be very livable.