We report the detection of the S(0) and S(1) pure rotational transitions of H-2 in emission from a boundary layer of the Taurus molecular cloud. These lines were observed with the Spitzer Infrared Spectrograph (IRS), and are very weak, with maximum specific intensity <= 0.4 MJy sr(-1). The emission is strongest 8.5' (0.33 pc) outside the edge of the cloud defined by the (CO)-C-13. We see H2 emission towards the bulk of the cloud at a lower level, suggestive of limb brightening of an envelope around the purely molecular cloud. The peak column densities looking directly towards the cloud are N(J = 3) = 1.3x10(17) cm(-2), and N(J = 2) = 2.2x10(18) cm(-2). Towards the maximum of the rotationally excited H-2 emission, N(J = 3) = 5.2x10(17) cm(-2) and N(J = 2) = 4.4x10(18) cm(-2). Interpreting the ratio is made difficult by the not well determined ortho- to para-H-2 ratio (OPR), but for reasonable values of the OPR, we can constrain the characteristics of the region responsible for the H2 emission. For example, for OPR = 3 and n(H-2) = 100 cm(-3), T-K must be greater than approximately 200 K. We have used the Meudon PDR code to model the H-2 emission from the cloud edge, and find that while the column density in J = 2 can be reproduced with reasonable parameters for the region and its environment, the column density in J = 3 that is predicted falls more than a factor of 5 below that observed. This suggests that an additional source of H-2 excitation is present. Further data and modeling are required to understand this issue, which will improve our understanding of cloud structure and the physics of H-2 formation.