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We show that non-Hermitian Ginibre random matrix behaviors emerge inspatially-extended many-body quantum chaotic systems in the space direction,just as Hermitian random matrix behaviors emerge in chaotic systems in the timedirection. Starting with translational invariant models, which can beassociated with dual transfer matrices with complex-valued spectra, we showthat the linear ramp of the spectral form factor necessitates that the dualspectra have non-trivial correlations, which in fact fall under theuniversality class of the Ginibre ensemble, demonstrated by computing the levelspacing distribution and the dissipative spectral form factor. As a result ofthis connection, the exact spectral form factor for the Ginibre ensemble can beused to universally describe the spectral form factor for translationalinvariant many-body quantum chaotic systems in the scaling limit where $t$ and$L$ are large, while the ratio between $L$ and $L_{\mathrm{Th}}$, the many-bodyThouless length is fixed. With appropriate variations of Ginibre models, weanalytically demonstrate that our claim generalizes to models withouttranslational invariance as well. The emergence of the Ginibre ensemble is agenuine consequence of the strongly interacting and spatially extended natureof the quantum chaotic systems we consider, unlike the traditional emergence ofHermitian random matrix ensembles.

Many-body quantum chaos and emergence of Ginibre ensemble