The vibrating-wire technique has been applied to design a viscometer for precise measurements on gases in the temperature range 25 to 250°C at pressures from 0.1 to 40 MPa employing two Chromel wires with different radii. The technique has been improved to avoid the influence of higher harmonic modes and the degeneracy of perpendicular modes, to eliminate electromagnetic noise from the signal, and to minimize the influence of the magnetic damping. The decrement and frequency of the oscillation have to be determined by extrapolation to zero displacement, and wires with a perfectly smooth surface are needed to meet the requirements of the measuring theory. The viscosity measurements are characterized by a precision of ±0.05% at ambient temperature. Considering the uncertainty of the reference data used for calibration, the total uncertainty amounts to ±0.2% within the calibrated range of the boundary-layer thickness.