To study the atomic , molecular and ionized emission of Giant Molecular Clouds ( GMCs ) in the Milky Way , we have initiated a Large Program with the Karl G. Jansky Very Large Array ( VLA ) : ‘ THOR - The H i , OH , Recombination Line survey of the Milky Way ’ . We map the 21cm H i line , 4 OH lines , up to 19 H \alpha recombination lines and the continuum from 1 to 2 GHz of a significant fraction of the Milky Way ( l = 15 \degr - 67 \degr , |b| \leq 1 \degr ) at an angular resolution of \sim 20 \arcsec . Starting in 2012 , we mapped 4 square degrees of the GMC associated with the W43 star-formation complex as a pilot study . The rest of the THOR survey area was observed during 2013 and 2014 . In this paper , we focus on the H i emission from the W43 GMC complex . Classically , the H i 21cm line is treated as optically thin with properties such as the column density calculated under this assumption . This approach might give reasonable results for regions of low-mass star-formation , however , it is not sufficient to describe giant molecular clouds . We analyzed strong continuum sources to measure the optical depth along the line of sight , and thus correct the H i 21cm emission for optical depth effects and weak diffuse continuum emission . Hence , we are able to measure the H i mass of this region more accurately and our analysis reveals a lower limit for the H i mass of M = 6.6 _ { -1.8 } \times 10 ^ { 6 } M _ { \odot } ( v _ { LSR } = 60 - 120 km s ^ { -1 } ) , which is a factor of 2.4 larger than the mass estimated with the assumption of optically thin emission . The H i column densities are as high as N _ { { { H \textsc { i } } } } \sim 150 M _ { \odot } pc ^ { -2 } \approx 1.9 \times 10 ^ { 22 } { cm ^ { -2 } } , which is an order of magnitude higher than for low mass star formation regions . This result challenges theoretical models that predict a threshold for the H i column density of \sim 10 M _ { \odot } pc ^ { -2 } , at which the formation of molecular hydrogen should set in . By assuming an elliptical layered structure for W43 , we estimate the particle density profile . For the atomic gas particle density , we find a linear decrease toward the center of W43 with values decreasing from n _ { { { H \textsc { i } } } } = 20 cm ^ { -3 } near the cloud edge to almost 0 cm ^ { -3 } at its center . On the other hand , the molecular hydrogen , traced via dust observations with the Herschel Space Observatory , shows an exponential increase toward the center with densities increasing to n _ { { H _ { 2 } } } > 200 cm ^ { -3 } , averaged over a region of \sim 10 pc . While at the cloud edge atomic and molecular hydrogen are well mixed , the center of the cloud is strongly dominated by H _ { 2 } emission . We do not identify a sharp transition between hydrogen in atomic and molecular form . Our results are an important characterization of the atomic to molecular hydrogen transition in an extreme environment and challenges current theoretical models .