A surgical suture is made of an elongate, hollow braid of high strength fibers. The braid defines an elongate, longitudinally-extending, central chamber that is open and without any core material extending therein so that, when a surgeon's knot is tied with the suture, the cross-sectional shape of the braid collapses upon itself and is reduced in size in response to pressures experienced when the knot is tightened thereby producing a low profile knot that resists slippage. Preferably, the braid is of a size corresponding to a USP size 5-0 to USP size 7 suture and has one or more, preferably a pair, of color contrasting monofilaments woven therein to enhance suture visibility. Methods of making a flattened suture and of utilizing the high strength suture to maintain body tissues in an engaged position to promote healing are also provided.