Fast radio bursts (FRBs) are highly dispersed millisecond-duration radio flashes probably arriving from far outside the Milky Way(1,2). This phenomenon was discovered at radio frequencies near 1.4 gigahertz and so far has been observed in one case(3) at as high as 8 gigahertz, but not at below 700 megahertz in spite of substantial searches at low frequencies(4-7). Here we report detections of 13 FRBs at radio frequencies as low as 400 megahertz, on the Canadian Hydrogen Intensity Mapping Experiment (CHIME) using the CHIME/FRB instrument(8). They were detected during a telescope pre-commissioning phase, when the sensitivity and field of view were not yet at design specifications. Emission in multiple events is seen down to 400 megahertz, the lowest radio frequency to which the telescope is sensitive. The FRBs show various temporal scattering behaviours, with the majority detectably scattered, and some apparently unscattered to within measurement uncertainty even at our lowest frequencies. Of the 13 reported here, one event has the lowest dispersion measure yet reported, implying that it is among the closest yet known, and another has shown multiple repeat bursts, as described in a companion paper(9). The overall scattering properties of our sample suggest that FRBs as a class are preferentially located in environments that scatter radio waves more strongly than in the diffuse interstellar medium in the Milky Way.