Methyl isocyanide (CH3NC) is the isocyanide with the largest number of atoms confirmed in the interstellar medium (ISM), but it is not an abundant molecule, having only been detected towards a handful of objects. Conversely, its isomer, methyl cyanide (CH3CN), is one of the most abundant complex organic molecules detected in the ISM, with detections in a variety of low- and high-mass sources. Aims: The aims of this work are to determine the abundances of methyl isocyanide in the solar-type protostellar binary IRAS 16293-2422 and to understand the stark abundance differences observed between methyl isocyanide and methyl cyanide in the ISM. Methods: We use Atacama Large Millimeter/submillimeter Array (ALMA) observations from the Protostellar Interferometric Line Survey (PILS) to search for methyl isocyanide and compare its abundance with that of its isomer methyl cyanide. We use a new line catalogue from the Cologne Database for Molecular Spectroscopy (CDMS) to identify methyl isocyanide lines. We also model the chemistry with an updated version of the three-phase chemical kinetics model MAGICKAL, presenting the first chemical modelling of methyl isocyanide to date. Results: We detect methyl isocyanide for the first time in a solar-type protostar, IRAS 16293-2422 B, and present upper limits for its companion protostar, IRAS 16293-2422 A. Methyl isocyanide is found to be at least 20 times more abundant in source B compared to source A, with a CH3CN/CH3NC abundance ratio of 200 in IRAS 16293-2422 B and >5517 in IRAS 16293-2422 A. We also present the results of a chemical model of methyl isocyanide chemistry in both sources, and discuss the implications for methyl isocyanide formation mechanisms and the relative evolutionary stages of both sources. The chemical modelling is unable to match the observed CH3CN/CH3NC abundance ratio towards the B source at densities representative of that source. The modelling, however, is consistent with the upper limits for the A source. There are many uncertainties in the formation and destruction pathways of methyl isocyanide, and it is therefore not surprising that the initial modelling attempts do not reproduce observations. In particular, it is clear that some destruction mechanism of methyl isocyanide that does not destroy methyl cyanide is needed. Furthermore, these initial model results suggest that the final density plays a key role in setting the abundance ratio. The next steps are therefore to obtain further detections of methyl isocyanide in more objects, as well as undertaking more detailed physico-chemical modelling of sources such as IRAS16293.