We report, for the first time, the observation of spontaneous parametric down-conversion (SPDC) free of phase matching (momentum conservation). We alleviate the need to conserve momentum by exploiting the position-momentum uncertainty relation and using a planar geometry source, a 6 μm thick layer of lithium niobate. Nonphase-matched SPDC opens up a new platform on which to investigate fundamental quantum effects but it also has practical applications. The ultrasmall thickness leads to a frequency spectrum an order of magnitude broader than that of phase-matched SPDC. The strong two-photon correlations are still preserved due to energy conservation. This results in ultrashort temporal correlation widths and huge frequency entanglement. The studies we make here can be considered as the initial steps into the emerging field of nonlinear quantum optics on the microscale and nanoscale.