Among all superconducting undulator geometries, a helical undulator provides a very compact geometry and further is more effective in producing synchrotron radiation, providing circularly polarized photons, which are widely usable for synchrotron radiation users. These characteristics make it a very attractive option for realizing more compact free-electron lasers, requiring a combination of short-period and high-field undulators to produce coherent light up to X-rays. To further increase the magnetic field at 4.2 K and achieve larger operating margins as compared with low-temperature superconductors, the application of a high-temperature superconductor (HTS) in the form of coated rare-Earth barium copper oxide tapes was investigated. This article presents the design and manufacturing work done on an HTS helical undulator prototype - the very first helical undulator design based on HTS tape winding to the best of the authors' knowledge. To provide proof of concept, a five-period short-model demonstrator was realized by a bifilar, no-insulation winding scheme from a single piece of HTS cable, wound with a period length of 13 mm and a magnetic gap of 5 mm. First powering tests at 77 K, performed in liquid nitrogen, revealed stable operations up to the calculated critical current of 140 A and even above. Higher currents of up to 160 A showed the expected coil protection, enabling the current to bypass the appearance of normal conducting zones and redistribute without degrading the superconductor.