This　paper　proposes　a　chaotic　jerk　system　coexisting　with　only　one　non-hyperbolic　equilibrium　with　one　zero　eigenvalue　and　a　pair　of　complex　conjugate　eigenvalues.　The　system　has　no　classical　Hopf　bifurcations　and　belongs　to　a　newly　category　of　chaotic　systems.　Based　on　the　averaging　theory,　an　analytic　proof　of　the　existence　of　zero-Hopf　bifurcation　is　exhibited.　Moreover,　unstable　periodic　orbits　from　the　zero-Hopf　bifurcation　are　obtained.　This　approach　may　be　useful　to　clarify　chaotic　attractors　with　non-hyperbolic　equilibrium　hidden　behind　complicated　phenomena.