DNA origami is one of the most promising recent developments in DNA self-assembly. It allows for the construction of arbitrary nanoscale patterns and objects by folding a long viral scaffold strand using a large number of short "staple" strands. Assembly is usually accomplished by thermal annealing of the DNA molecules in buffer solution. We here demonstrate that both 2D and 3D origami structures can be assembled isothermally by annealing the DNA strands in denaturing buffer, followed by a controlled reduction of denaturant concentration. This opens up origami assembly for the integration of temperature-sensitive components.