Oscillator with CMOS inverter - calculate elements
The design process is similar to a crystal oscillator, since the crystal will 'look' like an inductor in the steady state. 

You treat the gate as a high-impedance input/high-impedance output amplifier- the output as a current source that is controlled by the input voltage, so it's characterized by the transconductance. 

One requirement is that the transconductance multiplied by the product of the capacitor reactances must be > 1 at the desired frequency of oscillation to satisfy the Barkhausen criteria. Here is the typical transconductance of a 74LVU04 vs. supply voltage. 



At 3V (just say) the transconductance is about 30 mA/V. So C &lt; 0.22uF, and 0.1uF might be acceptable if you're using this particular chip at 3V or so, at 125kHz (or less). 

You also want resonance at 125kHz, and the capacitors are effectively in series for that calculation, so 0.05uF, and with a 1mH inductor it should resonate at 22.5kHz.