1. A method of determining a presence or absence of a fetal aneuploidy in a fetus by analysis of a maternal blood sample obtained from a pregnant woman comprising a mixture of fetal and maternal cells, the method comprising: (a) enriching a mixture of fetal and maternal cells of a maternal blood sample for fetal cells to obtain a mixed cell preparation enriched for fetal cells; (b) splitting the mixed cell preparation of step (a) into at least 100 discrete portions and directing the discrete portions to different locations; (c) identifying at least one location that contains a single fetal cell and obtaining genomic DNA from the single fetal cell at the at least one identified location; (d) amplifying fetal genomic DNA obtained from the single fetal cell at the at least one identified location; (e) sequencing the fetal genomic DNA of step (d) to generate sequence data; and (f) determining the presence or absence of a fetal aneuploidy from the sequence data of step (e), wherein said determining comprises analyzing the sequence data using computer executable logic recorded on a computer readable medium.