Don't panic! Chinchillas typically drink most, if not all, of their water at night. Use a rubber band to mark where the water is at and compare it tomorrow.
With my water bottle the level drops about 1 to 2 cm by morning. Mine is smaller in diameter than most so you will probably see less movement depending on its dimensions.
Every morning and evening check your waterer by pushing on the ball and make sure it is dispensing. Most water bottles can be finicky with temperature and pressure variations so take care to make sure it is working each day. If you have a gravity fed waterer it is more reliable. Gravity fed waterers have a valve inside. Normal water bottles have a ball.
Also the first day or two after relocating a chinchilla it will be quite stressed and eat and drink very little. After the first two weeks it will start acting differently, more like its normal self.
I'm glad your pet is friendly. Try not to overdo it for those first two weeks.
If you confirm your waterer is dispensing and there is no drop in water level overnight you may have a problem. Typically if a chinchilla has stopped drinking there will be other serious symptoms.
Have fun with your new pet.