Unfortunately, the study of Neviim Acharonim (the later prophets), and especially Trei Asar, has taken a 'back seat' in Jewish education. Hence, even though most of us have heard of the book of Chagai, rarely is it actually studied (even though it is only two chapters and written in very simple Hebrew).
However, anyone who has studied Chagai immediately sees its connection to the story of Chanuka. Take for example the pasuk:
"Take note from this day forward, from the 24th day of the ninth month (Kislev), from the day that the foundation was laid for the Lord's House - take note..." (Chagai 2:18)From this pasuk we see that the original construction of the second Temple began on the 24th (or 25th - see "Further Iyun") day of Kislev. Now if Chanuka marks the rededication of that very same Temple (after its defilement by the Greeks several hundred years later), then one can safely assume a thematic relationship between these two events.
Therefore, to uncover that relationship, we must begin our shiur with a quick overview of the time period of Chagai and Zecharya and their respective prophecies.
[This time period is commonly referred to as "shivat Tzion" - the return to Zion - when the Jews living within the Persian Empire had been given the right (by Cyrus) to return to Jerusalem and rebuild the Temple. (See Ezra 1:1-8 and Timeline.)]
[For the reader unfamiliar with these sources, it is recommended that you first read Sefer Chagai, Sefer Zecharya chapters 1-6, Ezra chapters 1, 3, and 4, and Yirmiyahu chapters 25 and 29.]