We present an analysis of the line-of-sight structure toward a sample of ten strong lensing cluster cores. Structure is traced by groups that are identified spectroscopically in the redshift range, 0.1 $leq$ z $leq$ 0.9, and we measure the projected angular and comoving separations between each group and the primary strong lensing clusters in each corresponding line of sight. From these data we measure the distribution of projected angular separations between the primary strong lensing clusters and uncorrelated large scale structure as traced by groups. We then compare the observed distribution of angular separations for our strong lensing selected lines of sight against the distribution of groups that is predicted for clusters lying along random lines of sight. There is clear evidence for an excess of structure along the line of sight at small angular separations ($theta leq 6$) along the strong lensing selected lines of sight, indicating that uncorrelated structure is a significant systematic that contributes to producing galaxy clusters with large cross sections for strong lensing. The prevalence of line-of-sight structure is one of several biases in strong lensing clusters that can potentially be folded into cosmological measurements using galaxy cluster samples. These results also have implications for current and future studies -- such as the Hubble Space Telescope Frontier Fields -- that make use of massive galaxy cluster lenses as precision cosmological telescopes; it is essential that the contribution of line-of-sight structure be carefully accounted for in the strong lens modeling of the cluster lenses.
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