Hitler was building the Third Reich. What were Reichs One and Two?

From The Straight Dope:

According to a fascinating tome called The Hitler Fact Book by Thomas Fuchs (like I say, I get the most amazing stuff in the mail), “the first Reich was the Holy Roman Empire of the Middle Ages; the second, the one established by Bismarck and ended by Germany’s defeat in 1918.” The term was a favorite of Hitler’s propaganda minister, Joseph Goebbels. Hitler himself wasn’t that crazy about it, Fuchs notes; he outlawed the term at the beginning of World War II and referred to his realm merely as the Reich.

(via Reddit)