We present results derived from four stellar occultations by the plutino object (208996) 2003~AZ, detected at January 8, 2011 (single-chord event), February 3, 2012 (multi-chord), December 2, 2013 (single-chord) and November 15, 2014 (multi-chord). Our observations rule out an oblate spheroid solution for 2003~AZ's shape. Instead, assuming hydrostatic equilibrium, we find that a Jacobi triaxial solution with semi axes $(470 \pm 20) \times (383 \pm 10) \times (245 \pm 8)b/a= 0.82 \pm 0.05c/a= 0.52 \pm 0.02$, can better account for all our occultation observations. Combining these dimensions with the rotation period of the body (6.75~h) and the amplitude of its rotation light curve, we derive a density $\rho=0.87 \pm 0.01^{-3}p_V= 0.097 \pm 0.009$. A grazing chord observed during the 2014 occultation reveals a topographic feature along 2003~AZ's limb, that can be interpreted as an abrupt chasm of width ~km and depth ~km or a smooth depression of width ~km and depth ~km (or an intermediate feature between those two extremes).

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