Methods and materials for detection of aneuploidy and other chromosomal abnormalities using fetal tissue are disclosed. Results can be obtained rapidly, without cell culture. The method uses digital PCR for amplification and detection of single target sequences, allowing an accurate count of a specific chromosome or chromosomal region. Specific polynucleic acid primers and probes are disclosed for chromosomes 1, 13, 18, 21, X and Y. These polynucleic acid sequences are chosen to be essentially invariant between individuals, so the test is not dependent on sequence differences between fetus and mother.