We report the first wide-field mapping of the kinematics and stellar populations in the E3 galaxy NGC 4365. The velocity maps extend previous long-slit work. They show two independent kinematic subsystems: the central 300 x 700 pc rotates about the projected minor axis, and the main body of the galaxy, 3 x 4 kpc, rotates almost at right angles to this. The line-strength maps show that the metallicity of the stellar population decreases from a central value greater than solar, to one-half solar at a radius of 2 kpc. The decoupled core and main body of the galaxy have the same luminosity-weighted age, of ~14 Gyr, and the same elevated magnesium-to-iron ratio. The two kinematically distinct components have thus shared a common star formation history. We infer that the galaxy underwent a sequence of mergers associated with dissipative star formation that ended >12 Gyr ago. The misalignment between the photometric and kinematic axes of the main body is unambiguous evidence of triaxiality. The similarity of the stellar populations in the two components suggests that the observed kinematic structure has not changed substantially in 12 Gyr.