How to filter low frequency noise on power supply from ChipCorder?
For starters, you haven't decoupled the microphone power at all. You should split R1 into two resistors (e.g., 4700&Omega; each), and put a fairly sizable ceramic capacitor (0.1 to 10.0 &micro;F; 1.0 &micro;F gives you a cutoff frequency of 34 Hz) from the middle junction to ground. This is the most direct path by which power supply noise can get into the audio input chain.

The next way would be if the opamp has poor PSRR, in which case, you should decouple its supply with a dedicated resistor and capacitor. The problem here is that you don't have a lot of headroom to work with, which will limit the size of the resistor you can use (voltage drop based on the average current that the opamp requires), which in turn will require a relatively large capacitor in order to get a low cutoff frequency.