We report the discovery of the first example of an Einstein zigzag lens, an extremely rare lensing configuration. In this system, J1721+8842, six images of the same background quasar are formed by two intervening galaxies, one at redshift z(1) = 0.184 and another at z(2) = 1.885. Two out of the six multiple images are deflected in opposite directions as they pass the first lens galaxy on one side and the second on the other side - the optical paths forming zigzags between the two deflectors. In this paper we demonstrate that J1721+8842, previously thought to be a lensed dual quasar, is in fact a compound lens, with the more distant lens galaxy also being distorted as an arc by the foreground galaxy. Evidence supporting this unusual lensing scenario includes: (1) identical light curves in all six lensed quasar images obtained from two years of monitoring at the Nordic Optical Telescope; (2) detection of the additional deflector at redshift z(2) = 1.885 in JWST/NIRSpec integral field unit data; and (3) a multiple-plane lens model reproducing the observed image positions. This unique configuration offers the opportunity to combine two major lensing cosmological probes, time-delay cosmography and dual source-plane lensing, since J1721+8842 features multiple lensed sources that form two distinct Einstein radii of different sizes, one of which is a variable quasar. We expect to place tight constraints on H-0 and w by combining these two probes of the same system. The z(2) = 1.885 deflector, a quiescent galaxy, is also the highest-redshift strong galaxy-scale lens with a spectroscopic redshift measurement known to date.