In this Letter we propose that coherent radio emission of Crab, other young energetic pulsars, and millisecond pulsars is produced in the magnetospheric current sheet beyond the light cylinder. We carry out global and local two-dimensional kinetic plasma simulations of reconnection to illustrate the coherent emission mechanism. Reconnection in the current sheet beyond the light cylinder proceeds in the very efficient plasmoid-dominated regime, and current layer gets fragmented into a dynamic chain of plasmoids which undergo successive coalescence. Mergers of sufficiently large plasmoids produce secondary perpendicular current sheets, which are also plasmoid-unstable. Collisions of plasmoids with each other and with the upstream magnetic field eject fast-magnetosonic waves, which propagate upstream across the background field and successfully escape from the plasma as electromagnetic waves that fall in the radio band. This model successfully explains many important features of the observed radio emission from Crab and other pulsars with high magnetic field at the light cylinder: phase coincidence with the high-energy emission, nano-second duration (nanoshots), and extreme instantaneous brightness of individual pulses.