The quantum kicked top has become a standard paradigm for theoretical studies of quantum chaos in spin systems. We describe the first experimental realization of a quantum kicked top using cold Cesium atoms interacting with laser and magnetic fields. The kicked top Hamiltonian can be accurately implemented using the nonlinear AC Stark shift and a pulsed magnetic field. Preparation of arbitrary initial states from a fiducial state can be achieved using Stark shifts and magnetic fields, Measurement of the complete spin density matrix is performed via Faraday rotation of a probe laser. A variety of interesting phenomena can be observed such as dynamical tunneling, rapid spreading of the wave function in the chaotic phase space, signatures of chaos in the evolution of nuclear-spin entanglement and robustness of the dynamics in the presence of decoherence. These dynamics can be understood by examining the Floquet eigenstates of the system.