The Torah portion is Miqeitz, Genesis 41:1-44:17. In synagogues using the Triennial system, 5785 is year 3 and the Torah reading is Genesis 43:16-44:17.
Joseph interprets Pharoah's dreams, predicts famine and provides the means to prepare, becomes a powerful man and marries. He is reunited with his brothers, who don't recognize him, and he tricks them.There is a special maftir portion (the final piece of the Torah reading) for Chanukah Day 3: Numbers 7:24-35. This portion lists the gifts given on the third day of another dedication: the Mishkan, the portable sanctuary in the wilderness.
The haftarah is I Kings 3:15-4:1. This is the well-known story of King Solomon, who says to divide a child in two to identify the real mother. It connects to the Torah portion because it begins with Solomon waking from a dream, as Joseph interpreted Pharaoh's dream.