Translation is the fundamental biological process converting mRNA information into proteins. Single-molecule imaging in live cells has illuminated the dynamics of RNA transcription; however, it is not yet applicable to translation. Here, we report single-molecule imaging of nascent peptides (SINAPS) to assess translation in live cells. The approach provides direct readout of initiation, elongation, and location of translation. We show that mRNAs coding for endoplasmic reticulum (ER) proteins are translated when they encounter the ER membrane. Single-molecule fluorescence recovery after photobleaching provides direct measurement of elongation speed (5 amino acids per second). In primary neurons, mRNAs are translated in proximal dendrites but repressed in distal dendrites and display "bursting" translation. This technology provides a tool with which to address the spatiotemporal translation mechanism of single mRNAs in living cells.