We present an analysis of the spatial distribution of star formation in a sample of 60 visually identified galaxy merger candidates at z > 1. Our sample, drawn from the 3D-HST survey, is flux limited and was selected to have high star formation rates based on fits of their broad-band, low spatial resolution spectral energy distributions. It includes plausible pre-merger (close pairs) and post-merger (single objects with tidal features) systems, with total stellar masses and star formation rates derived from multiwavelength photometry. Here we use near-infrared slitless spectra from 3D-HST which produce Hα or [O III] emission line maps as proxies for star formation maps. This provides a first comprehensive high-resolution, empirical picture of where star formation occurred in galaxy mergers at the epoch of peak cosmic star formation rate. We find that detectable star formation can occur in one or both galaxy centres, or in tidal tails. The most common case (58 per cent) is that star formation is largely concentrated in a single, compact region, coincident with the centre of (one of) the merger components. No correlations between star formation morphology and redshift, total stellar mass or star formation rate are found. A restricted set of hydrodynamical merger simulations between similarly massive and gas-rich objects implies that star formation should be detectable in both merger components, when the gas fractions of the individual components are the same. This suggests that z ~ 1.5 mergers typically occur between galaxies whose gas fractions, masses and/or star formation rates are distinctly different from one another.