Entangled states of many particles are of interest in quantum metrology, quantum information and quantum computing. Metrologically useful entangled states of large atomic ensembles have been generated, but these states display limited entanglement, as characterized by a non-negative Wigner function. Highly entangled states of massive particles have so far been produced and verified in small ensembles of ions. We have recently generated strong entanglement in a large atomic ensemble via the interaction with a weak light field and the detection of a single photon. We verify an entanglement depth(minimum number of mutually entangled atoms) of 1840 ± 70 out of 1930 particles, and reconstruct a negative-valued Wigner function of the many-body spin state, an important hallmark of strong nonclassicality. This is the first time a negative-valued Wigner function or the mutual entanglement of virtually all atoms have been attained in an ensemble containing more than a few particles. The entangled states produced can be used as inputs to atomic clocks and enable metrological gain. Our method can be extended to produce "Schrodinger's cat" states of many-atom ensemble.