An attempt is described to replace the present definition of the kilogram with the mass of a certain number of silicon atoms. A prerequisite for this is that the Avogadro constant, N_A, is determined with a relative uncertainty of better than 2 × 10⁻⁸. For the determination, silicon crystals are used. However, the difficulty arising thereby is the measurement of the average molar mass of natural Si. Consequently, a worldwide collaboration has been launched to produce approximately a 5 kg ²⁸Si single crystal with an enrichment factor greater than 99.985% and of sufficient chemical purity so that it can be used to determine N_A with the targeted relative measurement uncertainty mentioned above. In the following, the first successful tests of all technological steps will be reported (enrichment of SiF₄, distillation into silane and chemical purification, chemical vapour deposition of polycrystalline ²⁸Si, floating zone growth of a dislocation-free single crystal) and new equipment for the production of high-purity ²⁸Si with an enrichment of not less than 99.99% will be described. All steps are well defined by a Technical Road Map (TRM28) and all key results are measured by new mass spectrometric, IR spectroscopic and other chemical and physical methods, such as Hall effect, photoluminescence, laser scattering and x-ray topographic methods (TRM for Analytical Monitoring and Certification, TRM28-AMC). The initial enrichment of the gas is >0.999 95 and the depletion during the entire process is <0.000 05. The isotopic homogeneity is checked by natural Si crystal growth and does, in the enriched sphere, not exceed 5 × 10⁻¹⁰, relatively. The C content of the final material is less than 10¹⁵ atoms cm⁻³ and the specific resistance is 400–1000 Ω cm.