In this paper, autonomous 3rd order Josephson junction circuits containing angular variable are analyzed. For the sake of simplicity, easiness and accuracy the piecewise linearizing approximation is emplyed here. Using this method, Poincaré map, bifurcation diagram, attractor dimension and Lyapunov spectrum have been efficiently obtained especially for the chaos in this system. We have also observed the almost one-dimensional feature of the chaos orbit and the fine structure of the chaos oscillation. This chaos has a low attractor dimension nearly equal to that for the quasi-periodic oscillation in non-autonomous 2nd order JJ circuits.