We present unprecedented high-fidelity radio images of the M87 jet. We analyzed Jansky Very Large Array broadband full-polarization radio data from 4 to 18 GHz. The observations were taken with the most extended configuration (A configuration), which allows the study of the emission of the jet up to kiloparsec scales with a linear resolution of similar to 10 pc. The high sensitivity and resolution of our data allow us to resolve the jet width. We confirm a double-helix morphology of the jet material between similar to 300 pc and similar to 1 kpc. We found a gradient of the polarization degree with a minimum at the projected axis and maxima at the jet edges and a gradient in the Faraday depth with opposite signs at the jet edges. We also found that the behavior of the polarization properties along the wide range of frequencies is consistent with internal Faraday depolarization. All of these characteristics strongly support the presence of a helical magnetic field in the M87 jet up to 1 kpc from the central black hole, although the jet is most likely particle-dominated at these large scales. Therefore, we propose a plausible scenario in which the helical configuration of the magnetic field has been maintained to large scales thanks to the presence of Kelvin-Helmholtz instabilities.