Fluorescence resonance energy transfer (FRET) enables photosynthetic light harvesting(1), wavelength downconversion in light-emitting diodes(2) (LEDs), and optical biosensing schemes(3). The rate and efficiency of this donor to acceptor transfer of excitation between chromophores dictates the utility of FRET and can unlock new device operation motifs including quantum-funnel solar cells(4), non-contact chromophore pumping from a proximal LED5, and markedly reduced gain thresholds(6). However, the fastest reported FRET time constants involving spherical quantum dots (0.12-1 ns; refs 7-9) do not outpace biexciton Auger recombination (0.01-0.1 ns; ref. 10), which impedes multiexciton-driven applications including electrically pumped lasers(11) and carrier-multiplication-enhanced photovoltaics(12,13). Few-monolayerthick semiconductor nanoplatelets (NPLs) with tens-of-nanometre lateral dimensions(14) exhibit intense optical transitions(14) and hundreds-of-picosecond Auger recombination(15,16), but heretofore lack FRET characterizations. We examine binary CdSe NPL solids and show that interplate FRET (similar to 6-23 ps, presumably for co-facial arrangements) can occur 15-50 times faster than Auger recombination(15,16) and demonstrate multiexcitonic FRET, making such materials ideal candidates for advanced technologies.