The average B hadron lifetime was measured using data collected with the SLD detector at the SLC in 1993. From a sample of {approximately}50,000 Z{sup 0} events, a sample enriched in Z{sup 0} {yields} b{bar b} was selected by applying an impact parameter tag. The lifetime was extracted from the decay length distribution of inclusive vertices reconstructed in three dimensions. A binned maximum likelihood method yielded an average B hadron lifetime of {tau}{sub B} = 1.577 {plus_minus} 0.032(stat.) {plus_minus} 0.046(syst.) ps.