Vibrationally induced photodissociation in sulfurochloridic acid (HSO₃Cl) is found to be a viable process to form SO₃ and HCl from excitations of the OH-stretching overtone starting at ν_OH = 4. Reactive molecular dynamics simulations on a fully-dimensional potential energy surface fitted to MP2 calculations show that hydrogen transfer and HCl elimination compete with one another on the nanosecond time scale. Excitation with 5 and 6 quanta in the OH-stretch direct elimination of HCl is a dominant process on the several hundred picosecond time scale. At longer times, HCl formation is preceded by intramolecular hydrogen transfer and concomitant excitation of torsional degrees of freedom. As HSO₃Cl is a suitable proxy for H₂SO₄, which is relevant for weather and climate in the upper atmosphere, it is concluded that vibrationally induced photodissociation is a possible mechanism for H₂SO₄ decomposition. Final state energy distributions for different internal degrees of freedom are predicted which should be observable in laboratory measurements.