I'd use the +5Vsb of the PSU to power this. I made circuit for 2ndary PSUs on POC.net that allwed you to 1) run switch on 2ndary PSU when the PC's PSU was off with the standby LED, and another that allwed the +5Vsb to be used to power other small application devices.
There shold be a purple wire on the ATX connector (pin 9 if you know how to count the pins) this is you +5Vsb (+5V side band a.k.a. Standby) normall listed on the PSU specs as "+5vsb" nomrally the current is about 1A but an LED uses what 20mA at most and you can run it on 15mA (.015A) almost just a bright and 2x the life.
Example Spec sheet from a PSU (this is a 420 watt PSU)
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