The polymerase chain reaction (PCR) allows rapid amplification of DNA of known sequence. In many situations, part of a genetic sequence is known, but adjacent sequences of interest are unknown. This is common in investigations of antigen receptor genes from B and T lymphocytes, which are composed of a constant region of known sequence and a variable region, for which the sequence may not be known. Herein is described a method to amplify DNA when sequence information is available for only one primer. This procedure utilizes a primer of known sequence in conjunction with a mixture of short random primers. Application of this method to the amplification of T-cell antigen receptor cDNA is described.