The Chua's circuit satisfies the differential equations from Wikipedia.
Clearly, \$x=y=z=0\$ is a solution, but not the solution we see when double scroll appears. Since at \$t=0\$ when we switch on the circuit, \$x,y,z\$ must be all very close to \$0\$, for double scroll to appear, the system must be able to walk away from \$0\$. Therefore, \$0\$ must be an unstable equilibrium if the experiment is successful.
However, whether \$0\$ is an unstable equilibrium or not depends on the parameters. So does it mean that, if the parameters are incorrectly chosen so that \$0\$ is a stable equilibrium, then no double scroll can be observed?