My chin will sometimes be a little lethargic and stand-offish when she's sleepy. She'll just sit on a shelf and watch me rather than running over to me if I open up her cage during her "sleepy time" (which is usually in the afternoon). Is your chin exhibiting this lethargic behaviour all the time, or is it during a particular time of day? My chin usually perks up after a few minutes of interaction.
Do you have any other pets in the house, like dogs or cats? My chin used to sort of freeze if my cats were running around her cage a lot, presumably because she was frightened. When I recently got two new cats, she hung out on a corner shelf and didn't move around much for a couple days, presumably because the new kitties were stressing her out. Her usual behaviour and activity resumed after a couple days, though. Since you've only had your chin for a month, I wonder if she could perhaps just be a little stressed, as she's probably still adjusting to all the sights, sounds, and smells of your home. That stress could be compounded if you have any free-roaming pets she'd view as potential predators.
If she's lethargic all day and never or rarely perks up, or if you notice any other concerning symptoms (like a change in her eating/drinking/pooping habits, any unusual discharge from her nose/mouth/genitals, if her belly feels hard, etc.) then it's time for a vet visit.