Abstract The spatial variations of the velocity field of local stars provide direct evidence of Galactic differential rotation. The local divergence, shear and vorticity of the velocity field – the traditional Oort constants – can be measured based purely on astrometric measurements and in particular depend linearly on proper motion and parallax. I use data for 304 267 main-sequence stars from the Gaia DR1 Tycho-Gaia Astrometric Solution to perform a local, precise measurement of the Oort constants at a typical heliocentric distance of 230 pc. The pattern of proper motions for these stars clearly displays the expected effects from differential rotation. I measure the Oort constants to be: A = 15.3 ± 0.4 km s−1 kpc−1, B = −11.9 ± 0.4 km s−1 kpc−1, C = −3.2 ± 0.4 km s−1 kpc−1 and K = −3.3 ± 0.6 km s−1 kpc−1, with no colour trend over a wide range of stellar populations. These first confident measurements of C and K clearly demonstrate the importance of non-axisymmetry for the velocity field of local stars and they provide strong constraints on non-axisymmetric models of the Milky Way.