'Normal' galaxies observed at z>6, when the Universe was <1 billion years old, thus far show no evidence of the cold dust that accompanies star formation in the local Universe, where the dust-to-gas mass ratio is 1%. A prototypical example is 'Himiko' (z=6.6), which a mere 840 Myr after the Big Bang is forming stars at a rate of 30-100 Msun/yr, yielding a mass assembly time M^{star}/SFR 150x10^6 yr. Himiko is estimated to have a low fraction (2-3% of the Solar value) of elements heavier than helium (metallicity), and although its gas mass cannot be asserted at this time its dust-to-stellar mass ratio is constrained to be <0.05%. The local galaxy I Zw 18, with a metallicity 4% solar and forming stars less rapidly than Himiko but still vigorously for its mass (M^{star}/SFR 1.6x10^9 yr), is also very dust deficient and perhaps one of the best analogues of primitive galaxies accessible to detailed study. Here we report observations of dust emission from I Zw 18 from which we determine its dust mass to be 450-1800 Msun, yielding a dust-to-stellar mass ratio \approx 10^{-6}-10^{-5} and a dust-to-gas mass ratio 3.2-13x10^{-6}. If I Zw 18 is a reasonable analog of Himiko, then Himiko's dust mass is \approx 50,000 Msun, a factor of 100 below the current upper limit. These numbers are considerably uncertain, but if most high-z galaxies are more like Himiko than like the quasar host SDSS J114816.64+525150.3, then the prospects for detecting the gas and dust in them are much poorer than hitherto anticipated.