The Karlsruhe Tritium Neutrino (KATRIN) experiment aims to determine the absolute mass of the electron antineutrino from a precise measurement of the tritium β-spectrum near its endpoint at 18.6 keV with a sensitivity of 0.2 eV c⁻². KATRIN uses an electrostatic retardation spectrometer of MAC-E filter type for which it is crucial to monitor high voltages of up to 35 kV with a precision and long-term stability at the ppm level. Since devices capable of this precision are not commercially available, a new high voltage divider for direct voltages of up to 35 kV has been designed, following the new concept of the standard divider for direct voltages of up to 100 kV developed at the Physikalisch-Technische Bundesanstalt (PTB)^*. The electrical and mechanical design of the divider, the screening procedure for the selection of the precision resistors, and the results of the investigation and calibration at the PTB are reported here. During the latter, uncertainties at the low ppm level have been deduced for the new divider, thus qualifying it for the precision measurements of the KATRIN experiment.