Neanderthals are often considered as less technologically advanced than modern humans. However, we typically only find faunal remains or stone tools at Paleolithic sites. Perishable materials, comprising the vast majority of material culture items, are typically missing. Individual twisted fibres on stone tools from the Abri du Maras led to the hypothesis of Neanderthal string production in the past, but conclusive evidence was lacking. Here we show direct evidence of fibre technology in the form of a 3-ply cord fragment made from inner bark fibres on a stone tool recovered in situ from the same site. Twisted fibres provide the basis for clothing, rope, bags, nets, mats, boats, etc. which, once discovered, would have become an indispensable part of daily life. Understanding and use of twisted fibres implies the use of complex multi-component technology as well as a mathematical understanding of pairs, sets, and numbers. Added to recent evidence of birch bark tar, art, and shell beads, the idea that Neanderthals were cognitively inferior to modern humans is becoming increasingly untenable.