This paper describes a study of Bose-Einstein correlations made using the ALEPH detector at LEP. The correlations are found to enhance the two particle differential cross section for pairs of identical pions by a factor which can be roughly parametrized byR(Q)=1+λ exp(-Q2σ2), whereQ is the difference in the 3-momenta of the two pions in their centre of mass frame, λ=0.51±0.04±0.11 and σ=3.3±0.2±0.8 GeV−1, which corresponds to a source size of 0.65±0.04±0.16 fm. The large systematic errors on these results reflect their strong dependence on the choice of the reference sample used in the analysis. This problem is believed to occur primarily because of uncertainties in the rates of resonance production and a lack of knowledge about the pion-pion strong interaction. No significant correlations are seen amongst like-charged pion-kaon pairs.