  In recent years it has been speculated that in extreme low metallicity
galactic environments, stars form in regions that lack H2. In this paper we
investigate how changing the metallicity and UV-field strength of a galaxy
affects the star formation within, and the molecular gas Kennicutt-Schmidt
relation. Using extremely high resolution arepo simulations of isolated dwarf
galaxies, we independently vary the metallicity and UV-field to between 1% and
10% solar neighbourhood values. We include a non-equilibrium, time-dependant
chemical network to model the molecular composition of the ISM, and include the
effects of gas shielding from an ambient UV field. Crucially our simulations
directly model the gravitational collapse of gas into star-forming clumps and
cores and their subsequent accretion using sink particles. In this first
publication we find that reducing the metallicity and UV-field by a factor of
10 has no effect on star formation, and minimal effect on the cold, dense star
forming gas. The cold gas depletion times are almost an order of magnitude
longer than the molecular gas depletion time due to the presence of star
formation in HI dominated cold gas. We study the H2 Kennicutt-Schmidt
relationship that arises naturally within the simulations and find a near
linear power law index of N = 1.09 +/- 0.014 in our fiducial 10% solar
metallicity model. As the metallicity and UV-field are reduced this becomes
moderately steeper, with a slope of N = 1.24 +/- 0.022 for our 1% solar
metallicity and 1% solar UV field model.
