Why the DC voltmeter does not read zero when it measures an AC signal?(Chua's circuit)
Your voltmeter is probably showing DC offset because depending on how you built your Chua's circuit (and what it is doing at the moment) it will have a DC offset.

From your linked document:



It looks to me like a properly operating Chua's circuit can have offsets in various directions.

Outside of that, your circuit may be operating incorrectly (or not at all.)  You really need an oscilloscope to see what is going on.

If your Chua's circuit is supposed to operate at audio frequencies, you can get a free oscilloscope program for your PC (or smart phone) and have a look.  You'll probably need to add in a bit of circuitry to match signal levels and your audio input, but that should be easy enough to do - the software producer and the internet in general has a lot of info on "sound card oscilloscopes."