It is commonly anticipated that an insulating state collapses in favor of an emergent metallic state at high pressures as the unit cell shrinks and the electronic bandwidth broadens to fill the insulating energy band gap. Here we report a rare insulating state that persists up to at least 185 GPa in the antiferromagnetic iridate Sr2IrO4, which is the archetypical spin-orbit-driven Jeff = 1/2 insulator. This study shows the electrical resistance of single-crystal Sr2IrO4 initially decreases with applied pressure, reaches a minimum in the range, 32 -38 GPa, then abruptly rises to fully recover the insulating state with further pressure increases up to 185 GPa. Our synchrotron x-ray diffraction and Raman scattering data show the onset of the rapid increase in resistance is accompanied by a structural phase transition from the native tetragonal I41/acd phase to an orthorhombic Pbca phase (with much reduced symmetry) at 40.6 GPa. The clear-cut correspondence of these two anomalies is key to understanding the stability of the insulating state at megabar pressures: Pressureinduced, severe structural distortions prevent the expected metallization, despite the 26% volume compression attained at the highest pressure accessed in this study.Moreover, the resistance of Sr2IrO4 remains stable while the applied pressure is tripled from 61 GPa to 185 GPa. These results suggest that a novel type of electronic Coulomb correlation compensates the anticipated band broadening in strongly spin-orbit-coupled materials at megabar pressures. 3 It is well established that a rare interplay of on-site Coulomb repulsion, U, and strong spin-orbit interactions (SOI) has unique, intriguing consequences in 4d-and 5dtransition metal oxides [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The SOI-driven Jeff = ½ Mott insulating state in the 5dtransition metal oxide Sr2IrO4 is a profound manifestation of such an interplay [1, 2]. Sr2IrO4 adopts a canted antiferromagnetic (AFM) state [16] with a Néel temperature TN = 240 K [17-20] and an energy gap < 0.62 eV [21-23]. It exhibits key structural, electronic and magnetic features similar to those of La2CuO4, which has inspired expectations that novel superconductivity could emerge in Sr2IrO4 via electron doping [9]. However, there has been no experimental confirmation of superconductivity despite intensive experimental efforts [5].It has become increasingly clear that the conspicuous absence of superconductivity in Sr2IrO4 is due in part to structural distortions; in particular, IrO6 octahedral rotations play a crucial role in determining the ground state [5,16,24,25]. The inherently strong SOI in Sr2IrO4 locks the canted Ir moments to the IrO6 octahedra in a manner that is not seen in other materials, such as the cuprates [5,16,25,26].Despite the potential for broad and novel consequences of strong SOI in Sr2IrO4, the overwhelming balance of attention has been devoted to the possible existence of superconductivity [14]. The present work demonstrates a clear-cut, intriguing behavior of Sr2IrO4...