The deep equatorial track of the world ocean is subject to intense zonal flow fields that still remain to be better understood. Inertial instability has been invoked to explain some of its features. Here we present possible in situ imprints of such a mechanism in the equatorial Atlantic Ocean below the thermocline. We analyse the observed pattern of homogeneous density layers of 50--100 m vertical scale, which are characterized by a large meridional coherency up to 2¿ of latitude, a concentration in the vicinity of the equator and foremost a vertical localization within regions of well-mixed angular momentum (westward jets). These distinctive properties suggest inertial instability to be a plausible mechanism for this extended layering. Numerical simulations forced by a time-oscillating shear reproduce the observed density layering characteristics. The prescription of deep jets in the background flow controls the vertical localization of the layering inside westward jets.