We eat dairy foods on Channukah in memory of the miracle that occured through the milk that Judith fed to the enemy, who was one of the Grecian kings, as is recounted in the book 'Hemdat Yamim'. This miracle occured some years before the chief miracle of Channukah, but since the enemy was also a Grecian king, and he also wanted to make the Jews abandon their religion, we also commemorate this miracle during the days of Channukah. This is similar to the tradition of eating seeds on Purim to commemorate the miracle that occured to Daniel and his companions, peace be upon them. It seems to me, with God's help, that there is a hint in the word chalav, milk, that refers to the three mitzvot that the Greeks wanted to abolish, and over which the Jews were ready to sacrifice themselves: The first letter, chet, refers to the first letter of Chodesh, the calendar. The letter bet refers to the second letter of Shabbat. And the letter lamed refers to the third letter of Milah, the covenant of circumcision that they were forced to abandon.