Magnetic reconnection in current sheets is a magnetic-to-particle energy conversion process that is fundamental to many space and laboratory plasma systems. In the standard model of reconnection, this process occurs in a minuscule electron-scale diffusion region1,2. On larger scales, ions couple to the newly reconnected magnetic-field lines and are ejected away from the diffusion region in the form of bi-directional ion jets at the ion Alfvén speed3-5. Much of the energy conversion occurs in spatially extended ion exhausts downstream of the diffusion region 6 . In turbulent plasmas, which contain a large number of small-scale current sheets, reconnection has long been suggested to have a major role in the dissipation of turbulent energy at kinetic scales7-11. However, evidence for reconnection plasma jetting in small-scale turbulent plasmas has so far been lacking. Here we report observations made in Earth's turbulent magnetosheath region (downstream of the bow shock) of an electron-scale current sheet in which diverging bi-directional super-ion-Alfvénic electron jets, parallel electric fields and enhanced magnetic-to-particle energy conversion were detected. Contrary to the standard model of reconnection, the thin reconnecting current sheet was not embedded in a wider ion-scale current layer and no ion jets were detected. Observations of this and other similar, but unidirectional, electron jet events without signatures of ion reconnection reveal a form of reconnection that can drive turbulent energy transfer and dissipation in electron-scale current sheets without ion coupling.