  A search for charginos and neutralinos, predicted by supersymmetric theories,
is performed using a data sample of 182.1 pb-1 taken at a centre-of-mass energy
of 189 GeV with the OPAL detector at LEP. No evidence for chargino or
neutralino production is found. Upper limits on chargino and neutralino pair
production cross-sections are obtained as a function of the chargino mass, the
lightest neutralino mass and the second lightest neutralino mass. Within the
Constrained Minimal Supersymmetric Standard Model framework, and for a chargino
- neutralino mass difference of more than 5 GeV, the 95% confidence level lower
limits on the chargino mass are 93.6 GeV for tan{beta} = 1.5 and 94.1 GeV for
tan{beta} = 35. These limits are obtained assuming a universal scalar mass m_0
> 500 GeV. The corresponding limits for all m_0 are 78.0 and 71.7 GeV. The 95%
confidence level lower limits on the lightest neutralino mass, valid for any
value of tan{beta} are 32.8 GeV for m_0 > 500 GeV and 31.6 GeV for all m_0.
