One of the dream reactions in polymer chemistry is the bottom-up, self-assembled synthesis of polymer fabrics, with interwoven, one-dimensional fibres of monomolecular thickness forming planar pieces of textiles. We have made a major step towards realizing this goal by assembling sophisticated, quadritopic linkers into surface-mounted metal-organic frameworks. By sandwiching these quadritopic linkers between sacrificial metal-organic framework thin films, we obtained multi-heteroepitaxial, crystalline systems. In a next step, Glaser–Hay coupling of triple bonds in the quadritopic linkers yields linear, interwoven polymer chains. X-ray diffraction studies revealed that this topochemical reaction leaves the MOF backbone completely intact. After removing the metal ions, the textile sheets can be transferred onto different supports and imaged using scanning electron microscopy and atomic-force microscopy. The individual polymer strands forming the two-dimensional textiles have lengths on the order of 200 nm, as evidenced by atomic-force microscopy images recorded from the disassembled textiles.