  Transport is called nonreciprocal when not only the sign, but also the
absolute value of the current, depends on the polarity of the applied voltage.
It requires simultaneously broken inversion and time-reversal symmetries, e.g.,
by the interplay of spin-orbit coupling and magnetic field. So far, observation
of nonreciprocity was always tied to resistivity, and dissipationless
nonreciprocal circuit elements were elusive. Here, we engineer fully
superconducting nonreciprocal devices based on highly-transparent Josephson
junctions fabricated on InAs quantum wells. We demonstrate supercurrent
rectification far below the transition temperature. By measuring Josephson
inductance, we can link nonreciprocal supercurrent to the asymmetry of the
current-phase relation, and directly derive the supercurrent magnetochiral
anisotropy coefficient for the first time. A semi-quantitative model well
explains the main features of our experimental data. Nonreciprocal Josephson
junctions have the potential to become for superconducting circuits what
$pn$-junctions are for traditional electronics, opening the way to novel
nondissipative circuit elements.
