Well---what is your desired freq range? I don't know that you will find a single chip, but a state-variable lp topology can be made with one dual OTA* like an NE5517 and a few (well, several) more parts. Basically each OTA with a C load on the current output becomes an integrator, and you need two integrators and a summer for the filter. Noise and distortion will not be exemplary but it will be pretty cheap at least.
Actually I think there is a way to do it with just the OTA, taking advantage of the ability to make a positive-gain integrator as well as the more typical negative-gain one.
Is the control ultimately a voltage (or current)?
*OTA = operational transconductance amplifier, for those not familiar with the term: differential voltage in, bipolar single-ended current out, with the diff voltage-to-current conversion gain or so-called transconductance set by a control current. Typical commercial chips also have darlington emitter followers on board that can be used as unity-gain buffers.