Oceanic alternating zonal jets at depth have been detected ubiquitously in observations and ocean general circulation models (GCMs). Such oceanic jets are generally considered as being generated by purely oceanic processes. Here we explore a possible air-sea interaction induced by surface signatures of the deep zonal jets using an eddy-permitting coupled atmosphere-ocean GCM (CGCM). The 23-year CGCM integration reproduces bands of latitudinally-narrow alternating jets in the Southeast Pacific. They extend from the sea surface to well below the main thermocline and are embedded in the large-scale westward-flowing South Equatorial Current, the latter mostly confined above the thermocline. These jets generate fine-scale sea surface temperature (SST) anomalies through the advection of zonal temperature gradients. The atmospheric boundary layer appears to respond thermally to this fine-scale SST field, which induces fine-scale wind stress anomaly through atmospheric pressure adjustment, as indicated by a good spatial correlation between the SST Laplacian field and the fine-scale wind stress curl. A Sverdrup calculation on the wind stress field of the CGCM predicts fine-scale zonal currents driven by the meridional gradient of the fine-scale wind stress curl. The positions of these Sverdrup currents are generally coincident with those of the original zonal jets and the Sverdrup prediction explains roughly half of the amplitudes of the jets. While the original cause of the deep zonal jets simulated in our CGCM is unidentified, this analysis suggests that there is likely a positive air-sea feedback: the jets generate fine-scale wind stress curl that reinforces themselves through the Sverdrup dynamics.