LiFePO₄ is one of the most frequently studied positive electrode materials for lithium-ion batteries during the last years. Nevertheless, there is still an extensive debate on the mechanism of phase transformation. On the one hand this is due to the small energetic differences involved and hence the great sensitivity with respect to parameters such as size and morphology. On the other hand this is due to the lack of in situ observations with appreciable space and time resolution. Here we present scanning transmission X-ray microscopy measurements following in situ the phase boundary propagation within a LiFePO₄ single crystal along the (010) orientation during electrochemical lithiation/delithiation. We follow, on a battery-relevant timescale, the evolution of a two-phase-front on a micrometre scale with a lateral resolution of 30 nm and with minutes of time resolution. The growth pattern is found to be dominated by elastic effects rather than being transport-controlled.