Chanukah are days ולהלל להודות, to praise Hashem, and the Arizal teaches that they are days of הוד. The attribute of הוד is associated with healing (as is taught in the holy sefarim). This is another source that Chanukah is mesugal for healing (Shaar Yissaschar, Yemei Orah 14).
The Gemara (Bava Kama 85a) says, לרפאות לרופא רשות שנתנה מכאן, "From this pasuk... the doctors were given permission to heal." Some say that רשות hints at Chanukah, the holiday whose meals are a רשות, not obligatory. מכאן, from these meals, לרפאות לרופא רשות נתנה, comes healing to the Jewish nation.
A Yid from Komemius, Eretz Yisrael, tells that one day, he awoke and couldn't see clearly. Everything appeared fuzzy and double. Frightened by this sudden change in his vision, he immediately went to doctors, but after several examinations, they said there was no cure for his condition. This occurred during Chanukah. As he sat before the Chanukah lecht, he stared continuously at the lit menorah; tears were flowing as he poured out his heart to Hashem. His tefillos were answered, and his eyesight returned, to the amazement of the doctors. This isn't surprising because these are days of miracles and refuos, beyond and above the constraints of nature.
Reb Itzekel of Pshevorsk zt'l lived in Aix-les-Bains, France. The Rosh Yeshiva there was Reb Chaim Yitzchak Chaykin zt'l, a student of the Chofetz Chaim zt'l. A bachur in the yeshiva had a cancerous growth in his throat r”l. The doctors determined that surgery was the only chance for this bachur to survive. The problem was that the required surgery was very risky because the growth was in the neck, and a tiny error could be fatal. Reb Chaykin went to Reb Itzekel for advice. Reb Itzekel replied, "I still have wicks from Chanukah. [Chanukah was three weeks earlier]. Place the wicks on the bachur's neck. He should stay home for three days, and b'ezras Hashem, he will have a refuah sheleimah." The bachur did as instructed. After three days, he returned to the doctor for a checkup. The doctor was shocked at the results. He was fully healed!
Sifsei Tzaddik adds that this is the reason behind the custom of giving Chanukah gelt. It symbolizes the wealth that Hashem bestows upon us these days.
The Gemara (Shabbos 151b) writes, "We have a tradition that a young Torah scholar does not become poor." The Gemara asks that we see that they do become poor sometimes. The Gemara answers, "If it happens that they become poor, מיהדר לא אפתחה הדורי, they don't go around begging at doors." This means that they don't become so poor until they need to collect tzedakah. The Ahavas Yisrael of Vizhnitz zt'l explained the words of the Gemara מיהדר לא אפתחה אהדורי, that he doesn't go around the doors, as follows: "He wasn't careful to light the Chanukah lecht in the doorway with proper hidur mitzvah." The Gemara is saying that a Torah scholar doesn't become poor. If he does, it is a sign that he wasn't cautious about lighting Chanukah lecht with the proper hidur mitzvah.
Chazal (Beitzah 32b) say, "Whoever has to come onto the table of others, the world is dark for him." On Chanukah, there is light. This means that in the merit of the lights of Chanukah, there will be parnassah, and everyone will be self-sufficient. No one will feel that the world is dark for him.
A grandson of the Divrei Chaim zt'l was poor and was forced to collect money to support his family. At one home, the homeowner said, "I will ask you a question, and if you give a satisfactory answer, I will give you a nice sum of money."
