Nichols was born Mikhail Igor Peschkowsky on November 6, 1931, in Berlin, Germany, the son of Brigitte (née Landauer) and Pavel Peschkowsky, a physician. His father was born in Vienna, Austria, to a Russian-Jewish immigrant family. Nichols' father's family had been wealthy and lived in Siberia, leaving after the Russian Revolution, and settling in Germany around 1920. Nichols' mother's family were German Jews. His maternal grandparents were Gustav Landauer, a leading theorist on anarchism, and author Hedwig Lachmann. Nichols was a third cousin twice removed of scientist Albert Einstein, through Nichols' mother.