We present an extinction map of the Large Magellanic Cloud ( LMC ) , using 204,502 stars from the Two Micron All Sky Survey point source catalog . We first use the NICE method to determine the reddening distribution , E ( H - K ) and E ( J - H ) , which we compare to the HI distribution to find a near-infrared reddening law of E ( J - H ) / E ( H - K ) = 1.20 \pm 0.04 . A visual extinction map ( \sim 6 ^ { \circ } \times 6 ^ { \circ } ) of the LMC is created using the NICER method ; at 4 arcmin resolution , a mean value of \mbox { $A _ { V } $ } = 0.38 mag is found . We derive the LMC CO-to-H _ { 2 } conversion factor , X _ { \mathrm { LMC } } , independent of assumptions about the virialization of giant molecular clouds , by comparing the NICER extinction map with NANTEN ^ { 12 } CO observations . In regions where \mbox { $A _ { V } $ } > 1 mag and ^ { 12 } CO emission is \geq 2 K km s ^ { -1 } , we measure X _ { \mathrm { LMC } } = 9.3 \pm 0.4 \times 10 ^ { 20 } ~ { } \mbox { cm$ { } ^ { -2 } $ ( K km s$ { } ^ { -1 } $% ) $ { } ^ { -1 } $ } . In the same regions , the LMC contains a total molecular mass of ( 4.5 \pm 0.2 ) \times 10 ^ { 7 } ~ { } M _ { \odot } .