  Methyl isocyanate (CH$_{3}$NCO) belongs to a select group of interstellar
molecules considered to be relevant precursors in the formation of larger
organic compounds, including those with peptide bonds. The molecule has only
been detected in a couple of high-mass protostars and potentially on comets. A
formation route on icy grains has been postulated for this molecule but
experimental evidence is lacking. Here we extend the range of environments
where methyl isocyanate is found, and unambiguously identify CH$_{3}$NCO
through the detection of 43 unblended transitions in the ALMA Protostellar
Interferometric Line Survey (PILS) of the low mass solar-type protostellar
binary IRAS 16293-2422. The molecule is detected toward both components of the
binary with a ratio HNCO/CH$_3$NCO $\sim$4--12. The isomers CH$_{3}$CNO and
CH$_3$OCN are not identified, resulting in upper abundance ratios of
CH$_{3}$NCO/CH$_{3}$CNO > 100 and CH$_{3}$NCO/CH$_3$OCN > 10. The resulting
abundance ratios compare well with those found for related N-containing species
toward high-mass protostars. To constrain its formation, a set of cryogenic UHV
experiments is performed. VUV irradiation of CH$_{4}$:HNCO mixtures at 20 K
strongly indicate that methyl isocyanate can be formed in the solid-state
through CH$_{3}$ and (H)NCO recombinations. Combined with gas-grain models that
include this reaction, the solid-state route is found to be a plausible
scenario to explain the methyl isocyanate abundances found in IRAS 16293-2422.
