A discrete time crystal (DTC) was experimentally observed in a spin chain of trapped atomic ions under a periodic Floquet-MBL Hamiltonian. The system, composed of 10 ions, was subjected to a sequence of Hamiltonians that included a global spin flip, long-range Ising interactions, and strong disorder. The study demonstrated robust sub-harmonic temporal responses, indicating the emergence of a DTC, which is a phase of matter where time translation symmetry is spontaneously broken. The DTC was found to be resilient to external perturbations and exhibited persistent oscillations and synchronization of interacting spins. The key ingredients for the DTC were strong drive, interactions, and disorder, which were implemented through a carefully designed Floquet Hamiltonian. The system's dynamics were analyzed using time-resolved measurements of spin magnetization, revealing sub-harmonic responses that persisted even under moderate perturbations. The phase boundary between the DTC and a symmetry-unbroken phase was determined by measuring the variance of the sub-harmonic peak amplitude. The results showed that the DTC phase transitions into a symmetry-unbroken MBL phase at large perturbations. The study provides a platform for exploring out-of-equilibrium quantum dynamics and novel phases of matter, including potential applications in quantum information tasks. The findings highlight the robustness of DTCs and their potential for studying long-range spatial-temporal correlations in non-equilibrium systems.A discrete time crystal (DTC) was experimentally observed in a spin chain of trapped atomic ions under a periodic Floquet-MBL Hamiltonian. The system, composed of 10 ions, was subjected to a sequence of Hamiltonians that included a global spin flip, long-range Ising interactions, and strong disorder. The study demonstrated robust sub-harmonic temporal responses, indicating the emergence of a DTC, which is a phase of matter where time translation symmetry is spontaneously broken. The DTC was found to be resilient to external perturbations and exhibited persistent oscillations and synchronization of interacting spins. The key ingredients for the DTC were strong drive, interactions, and disorder, which were implemented through a carefully designed Floquet Hamiltonian. The system's dynamics were analyzed using time-resolved measurements of spin magnetization, revealing sub-harmonic responses that persisted even under moderate perturbations. The phase boundary between the DTC and a symmetry-unbroken phase was determined by measuring the variance of the sub-harmonic peak amplitude. The results showed that the DTC phase transitions into a symmetry-unbroken MBL phase at large perturbations. The study provides a platform for exploring out-of-equilibrium quantum dynamics and novel phases of matter, including potential applications in quantum information tasks. The findings highlight the robustness of DTCs and their potential for studying long-range spatial-temporal correlations in non-equilibrium systems.