Disclosed is a method to achieve digital quantification of DNA (i.e., counting differences between identical sequences) using direct shotgun sequencing followed by mapping to the chromosome of origin and enumeration of fragments per chromosome. The preferred method uses massively parallel sequencing, which can produce tens of millions of short sequence tags in a single run and enabling a sampling that can be statistically evaluated. By counting the number of sequence tags mapped to a predefined window in each chromosome, the over- or under-representation of any chromosome in maternal plasma DNA contributed by an aneuploid fetus can be detected. This method does not require the differentiation of fetal versus maternal DNA. The median count of autosomal values is used as a normalization constant to account for differences in total number of sequence tags is used for comparison between samples and between chromosomes.