This work is the first study on the 3D shape of starbursting extremely metal-poor galaxies (XMPs; a galaxy is said to be an XMP if its ionized gas-phase metallicity is less than 1/10 the solar value). A few hundred XMPs have been identified in the local universe primarily through mining the spectroscopic catalog of the Sloan Digital Sky Survey (SDSS), and follow-up observations have shown that metallicity drops significantly at the starburst (compared to the quiescent component of the galaxy). As the timescale for gas mixing is short, the metal-poor gas triggering the starburst must have been accreted recently. This is strong observational evidence for the cold flow accretion predicted by cosmological models of galaxy formation, and, in this respect, XMPs seem to be the best local analogs of the very first galaxies.The ellipsoidal shape of a class of galaxies can be inferred from the observed axial ratio (q) distribution (q = minor axis/major axis) of a large sample of randomly-oriented galaxies. Fitting ellipses to 200 XMPs using r-band SDSS images, we observe that the axial ratio distribution falls off at q < ~0.4 and q > ~0.8, and we determine that these falloffs are not due to biases in the data. The falloff at low axial ratio indicates that the XMPs are thick for their size, and the falloff at high axial ratio suggests the vast majority of XMPs are triaxial. We also observe that smaller XMPs are thicker in proportion to their size, and it is expected that for decreasing galaxy size the ratio of random to rotational motions increases, which correlates with increasing relative thickness. The XMPs are low-redshift dwarf galaxies dominated by dark matter, and our results are compatible with simulations that have shown dark matter halos to be triaxial, with triaxial stellar distributions for low-mass galaxies and with triaxiality increasing over time. We will offer precise constraints on the 3D shape of XMPs via Bayesian analysis of our observed axial ratio distribution.This work has been supported by the La Caixa Foundation and the Estallidos Spanish Ministry of Science and Innovation grant.