A solid-solid phase transition of colloidal hard spheres confined between two planar hard walls is studied using a combination of molecular dynamics and Monte Carlo simulation. The transition from a solid consisting of five crystalline layers with square symmetry (5□) to a solid consisting of four layers with triangular symmetry (4△) is shown to occur through a nonclassical nucleation mechanism that involves the initial formation of a precritical liquid cluster, within which the cluster of the stable 4△ phase grows. Free-energy calculations show that the transition occurs in one step, crossing a single free-energy barrier, and that the critical nucleus consists of a small 4△ solid cluster wetted by a metastable liquid. In addition, the liquid cluster and the solid cluster are shown to grow at the planar hard walls. We also find that the critical nucleus size increases with supersaturation, which is at odds with classical nucleation theory. The △-solid-like cluster is shown to contain both face-centered-cubic and hexagonal-close-packed ordered particles. The kinetics of phase transitions plays an important role in condensed-matter physics and materials science. In order to gain a better fundamental understanding of how to control self-assembly processes in the fabrication of novel structures, many experimental and simulation studies have been devoted to colloidal systems. Experiments [1-4] and computer simulations [5][6][7] on bulk hard-sphere colloids suggested that the metastable fluid crystallizes and superheated crystals melt via a single-step nucleation process that is well described by classical nucleation theory (CNT) [8]. However, Ostwald's step rule suggests that the kinetic pathway to the most stable state can initially proceed through the nucleation of intermediate, metastable phases [9]. The effect of a nearby metastable state on nucleation and the occurrence of multistep nucleation processes have been studied in the crystallization of a range of systems including colloids [10,11], proteins [12], and patchy particles [13], and in the crystallization of molecular solids from solution [14].In contrast, the kinetic processes of solid-solid phase transitions, which involve complex structural rearrangements [15], have received considerably less attention [16]. Solid-solid transitions usually occur in a martensitic fashion [17,18] involving the concerted, diffusionless motion of the atoms in the unit cell. Anisotropic stress, rapid quenching, and a small system size have been found to promote martensitic transformations [19]. In colloids, martensitic transitions have been observed in small crystalline clusters [20][21][22] or lattices stretched by external fields [18,[23][24][25]. A solid-solid transition involving an activated nucleation process has recently been experimentally observed at the single-particle level for the first time in colloidal thin-film crystals confined between two glass plates [26]. The equilibrium phase diagram of hard spheres confined between two planar hard walls shows an alternati...