The invention provides methods of assembling a DNA molecule having a desired sequence. The methods involve contacting a DNA ligase with a plurality of short oligonucleotides to be assembled and performing the ligase chain reaction to thereby generate a set of polynucleotides. Oligonucleotides in the plurality overlap with and are complementary to a sequence of at least one other oligonucleotide in the plurality, and at least 50% of the oligonucleotides in the plurality are 6-30 nucleotides in length. The set of polynucleotides produced are contacted with a DNA polymerase and dNTPs in a mixture to join the set of polynucleotides and thereby create a DNA molecule having a desired sequence by polymerase chain assembly. The method allows for production of oligonucleotides of any length having very high sequence fidelity to a desired sequence.