We present ^ { 12 } CO J = 1 \rightarrow 0 and J = 2 \rightarrow 1 observations of the low metallicity ( 12 + log ( O/H ) = 7.74 ) Local Group dwarf irregular galaxy WLM made with the 15 m SEST and 14 m FCRAO telescopes . Despite the presence a number of HII regions , we find no CO emission . We obtain low upper limits on the integrated intensity ( I _ { CO } \leq 0.18 K km s ^ { -1 } for CO ( 1 \rightarrow 0 ) ) . The non-detection is consistent with the result of Taylor , Kobulnicky & Skillman ( [ 1998 ] ) , that dwarf galaxies below a metallicity of \sim 7.9 are not detected in CO emission . WLM shows that this trend continues for low metallicity galaxies even as their metallicities approach 7.9 . These results are consistent with the models of the metal poor ISM by Norman & Spaans ( [ 1997 ] ) . By comparing our CO data with observations of star formation in WLM , we find evidence for a high CO to H _ { 2 } conversion factor .