Although grand-design spiral galaxies are relatively common in the local Universe, only one has been spectroscopically confirmed to lie at redshift z > 2 (HDFX 28; z = 2.011); and it may prove to be a major merger that simply resembles a spiral in projection. The rarity of spirals has been explained as a result of disks being dynamically `hot' at z > 2 (refs 2-5), which may instead favour the formation of commonly observed clumpy structures. Alternatively, current instrumentation may simply not be sensitive enough to detect spiral structures comparable to those in the modern Universe. At z < 2, the velocity dispersion of disks decreases, and spiral galaxies are more numerous by z ~ 1 (refs 7, 13-15). Here we report observations of the grand-design spiral galaxy Q2343-BX442 at z = 2.18. Spectroscopy of ionized gas shows that the disk is dynamically hot, implying an uncertain origin for the spiral structure. The kinematics of the galaxy are consistent with a thick disk undergoing a minor merger, which can drive the formation of short-lived spiral structure. A duty cycle of <100 Myr for such tidally induced spiral structure in a hot massive disk is consistent with its rarity.