LaGaO3 single crystals, grown by the method of zone melting without a crucible, with radiation heating, were investigated by X-ray topography and diffractometry. It has been found that at 293 K these crystals have an orthorhombic unit cell with a = 5.520(2), b = 5.490(2), c=7.770 (I)A and twinning in the { 110}/(IT0) and { 112}/(1]-0) systems simultaneously. Regions of cross-twinning have been discovered in these systems. A first-order phase transition from orthorhombic to rhombohedral has been observed at 412.5K, the cell parameters being a=3.889A, = 89.50 ° (423 K). The rhombohedral phase has a developed twin structure in the {100}/(001) and {110}/(001) systems. During transformation the structure undergoes an inherited change to the twin structure of the orthorhombic phase.