We present a sensitive 870 µm survey of the Extended Chandra Deep Field South ( ECDFS ) combining 310 hours of observing time with the Large Apex BOlometer Camera ( LABOCA ) on the APEX telescope . The LABOCA ECDFS Submillimetre Survey ( LESS ) covers the full 30 ^ { \prime } \times 30 ^ { \prime } field size of the ECDFS and has a uniform noise level of \sigma _ { 870 \mu { m } } \approx 1.2 mJy beam ^ { -1 } . LESS is thus the largest contiguous deep submillimetre survey undertaken to date . The noise properties of our map show clear evidence that we are beginning to be affected by confusion noise . We present a catalog of 126 submillimetre galaxies ( SMGs ) detected with a significance level above 3.7 \sigma , at which level we expect 5 false detections given our map area of 1260 arcmin ^ { 2 } . The ECDFS exhibits a deficit of bright SMGs relative to previously studied blank fields but not of normal star-forming galaxies that dominate the extragalactic background light ( EBL ) . This is in line with the underdensities observed for optically defined high redshift source populations in the ECDFS ( BzKs , DRGs , optically bright AGN and massive K-band selected galaxies ) . The differential source counts in the full field are well described by a power law with a slope of \alpha = -3.2 , comparable to the results from other fields . We show that the shape of the source counts is not uniform across the field . Instead , it steepens in regions with low SMG density . Towards the highest overdensities we measure a source-count shape consistent with previous surveys . The integrated 870µm flux densities of our source-count models down to S _ { 870 \mu { m } } = 0.5 mJy account for > 65 \% of the estimated EBL from COBE measurements . We have investigated the clustering of SMGs in the ECDFS by means of a two-point correlation function and find evidence for strong clustering on angular scales < 1 ^ { \prime } with a significance of 3.4 \sigma . Assuming a power law dependence for the correlation function and a typical redshift distribution for the SMGs we derive a characteristic angular clustering scale of \theta _ { 0 } = 14 ^ { \prime \prime } \pm 7 ^ { \prime \prime } and a spatial correlation length of r _ { 0 } = 13 \pm 6 h ^ { -1 } Mpc .