The free-stream coherent structure theory developed by Deguchi & Hall (J. Fluid Mech., vol. 752, 2014, pp. 602–625), valid in the large-Reynolds-number asymptotic limit, is extended and applied to jet flows. It is shown that a nonlinear exact coherent structure can be supported at the edge of the jet, and the structure induces a much bigger streaky flow in the centre of the jet. The lambda-shaped vortices that characterise the coherent structure are qualitatively consistent with those seen in experimental observations. Here a planar incompressible jet is investigated for the sake of simplicity, but the structure we describe could be used as a basis of more complex theories for incompressible and compressible jets of practical importance.