Fan making a squealing sound when on

Just moved into a new apartment and to my horror, there's a slight but incredibly irritating squealing sound when the fan is running. Doesn't matter if the compressor is running, only the fan. It reminds me of the squeal that used to come from CRT monitors or TVs as they failed.

It could be airflow, maybe, but my feeling is that it's more consistent than that. Maybe something in the electronics? At any rate, I've filed a maintenance request, so we'll see what comes of that. In the meantime, does anyone have any ideas?