I know Hindenburg decides to run for a second term in order to prevent Hitler becoming president, but why does he then turn around and appoint him chancellor?
The political situation in Germany was deteriorating quickly. No functional majority government could be formed in parliament, and a succession of chancelors appointed by Hindenburg had failed to achieve anything. The communists were gaining in the public opinion and were fighting with the nazis in the streets. Hindenburg's advisers thought that they could control Hitler, who seemed politically inept. They convinced Hindenburg to put the nazis in power so that there wouldn't be a civil war.