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You either need dual supply or a DC bias for U1 non-inverting input.
Furthermore Q1 CB diode junction doesn't work as a noise source because it has high breakdown voltage. Use EB diode instead.
Assuming you can live with a response roll off at very low frequencies, add a capacitor at the ground end of R34 (value depends on LF roll off but I would suggest 47uF) then add a 330K resistor from pin 3 of U1 to +5V. Personally, I would increase the feedback resistors, all of them to at least 100K.
Brian.