We present results derived from four stellar occultations by the plutino object (208996) 2003~AZ$_{84}$, 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$_{84}$s shape. Instead, assuming hydrostatic equilibrium, we find that a Jacobi triaxial solution with semi axes $(470 pm 20) times (383 pm 10) times (245 pm 8)$~km % axis ratios $b/a= 0.82 pm 0.05$ and $c/a= 0.52 pm 0.02$, 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 $rho=0.87 pm 0.01$~g~cm$^{-3}$ a geometric albedo $p_V= 0.097 pm 0.009$. A grazing chord observed during the 2014 occultation reveals a topographic feature along 2003~AZ$_{84}$s limb, that can be interpreted as an abrupt chasm of width $sim 23$~km and depth $> 8$~km or a smooth depression of width $sim 80$~km and depth $sim 13$~km (or an intermediate feature between those two extremes).
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