We present measurements of the angular correlation function of galaxies selected from the first field of the H-ATLAS survey. Careful removal of the background from galactic cirrus is essential, and currently dominates the uncertainty in our measurements. For our 250 μm-selected sample we detect no significant clustering, consistent with the expectation that the 250 μm-selected sources are mostly normal galaxies at z ⪉ 1. For our 350 μm and 500 μm-selected samples we detect relatively strong clustering with correlation amplitudes A of 0.2 and 1.2 at 1', but with relatively large uncertainties. For samples which preferentially select high redshift galaxies at z~2-3 we detect significant strong clustering, leading to an estimate of r0 ~ 7-11 h-1 Mpc. The slope of our clustering measurements is very steep, δ ~ 2. The measurements are consistent with the idea that sub-mm sources consist of a low redshift population of normal galaxies and a high redshift population of highly clustered star-bursting galaxies. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.