What is the purpose of using a 1M Ohm resistor across crystal pins? Please refer to the image for clarity. The crystal serves as the clock source for an USB Hub device(LAN9512). There is nothing mentioned in the HUB datasheet about this, I suppose they have added it based on their experience, I have no clue about it. 
Answer
I found this document (Schematic Checklist), from the chip manufacturer (Microchip) which states (note point 5).
Usually something like a high-value bias resistor is supplied internally for a Pierce oscillator configuration typically used on IC crystal oscillators, but some ICs don't have them, and perhaps this chip either does not have one, or the ones on that chip revision were considered inadequate for some reason. That's speculation on my part, but the bottom line is that if Microchip says to use it, you'd better use it.
The bias resistor (internal or external) is required for the oscillator to reliably start up- it biases the amplifier into the linear region where noise can be amplified to get the crystal oscillator going.
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