A method of forming a compressible contact structure on a semi-conductor chip which comprises bonding a compressible polymer layer to the chip's surface, forming a plurality of openings within the layer, depositing electrically conductive material within the openings to form electrical connections with the chip's contacts, forming a plurality of electrically conductive line elements on the polymer layer extending from a respective opening and each including an end portion, and forming a plurality of contact members each on a respective one of the line segment end portions. The compressible polymer layer allows the contact members to deflect toward (compress) the chip when the contact members are engaged by an external force or forces. A semi-conductor chip including such a compressible contact structure is also provided.