  We present sensitive molecular line observations of the metal-poor blue
compact dwarf I Zw 18 obtained with the IRAM Plateau de Bure interferometer.
These data constrain the CO J=1-0 luminosity within our 300 pc (FWHM) beam to
be L_CO < 1 \times 10^5 K km s^-1 pc^2 (I_CO < 1 K km s^-1), an order of
magnitude lower than previous limits. Although I Zw 18 is starbursting, it has
a CO luminosity similar to or less than nearby low-mass irregulars (e.g. NGC
1569, the SMC, and NGC 6822). There is less CO in I Zw 18 relative to its
B-band luminosity, HI mass, or star formation rate than in spiral or dwarf
starburst galaxies (including the nearby dwarf starburst IC 10). Comparing the
star formation rate to our CO upper limit reveals that unless molecular gas
forms stars much more efficiently in I Zw 18 than in our own galaxy, it must
have a very low CO-to-H_2 ratio, \sim 10^-2 times the Galactic value. We detect
3mm continuum emission, presumably due to thermal dust and free-free emission,
towards the radio peak.
