Mine too. It had a chirping noise (chirp-chirp-chirp-etc) right after the initial system update but I haven't heard it since.
I couldn't ignore it though and went to the official board and read huge threads where they finally seemed to conclude that all XB1s had this or similar weird sound at the dashboard when idle, with no disc is in the drive or no app is in suspend, and it all started right after the update. The threads are still on fire though with all the new tier 2 launches. MS is clueless though and blindly tell people to send them in for repair and sends out refurbished ones, and the people that sent them away for repair all got ones without noise before the initial update but everyone started chirping again after the update. Send them in for repair again is MSs response.
So fortunately it seems to be a software issue. People had seen the same thing happen with 5 consoles on a row. No chirping before the update - chirping after the update. The official board's guessing is that it has to do with the power usage, and no Kinect connected, when the power usage is too low (idle at the dash with nothing suspended and no Kinect etc) a fan or something makes a weird chirping noise from running at an odd rpm or starting and stopping irregularly or something like that, and when the power usage goes up (disc in drive, Kinect connected etc) the chirping goes away.
So anyone with weird sounding consoles. Before sending the console to MS, try activating accessories and having apps on suspend or a disc in the drive and see if the noise goes away. Seems to fix the issue for most judging by the talk on the official board where there are huge threads about this.
Mine isn't chirping anymore even when idle on the dash though, but maybe it's enough for the power usage so to have wifi on or connecting two controllers and a remote? I guess it's possible that I might've missed if MS has rolled out a new update just now too if everything is updated in standby.