52: Early in the morning on the twenty-fifth day of the ninth month, which is the month of Chislev, in the one hundred and forty-eighth year,
53: they rose and offered sacrifice, as the law directs, on the new altar of burnt offering which they had built.
54: At the very season and on the very day that the Gentiles had profaned it, it was dedicated with songs and harps and lutes and cymbals.
55: All the people fell on their faces and worshiped and blessed Heaven, who had prospered them.
56: So they celebrated the dedication of the altar for eight days, and offered burnt offerings with gladness; they offered a sacrifice of deliverance and praise.
57: They decorated the front of the temple with golden crowns and small shields; they restored the gates and the chambers for the priests, and furnished them with doors.
58: There was very great gladness among the people, and the reproach of the Gentiles was removed.
59: Then Judas and his brothers and all the assembly of Israel determined that every year at that season the days of dedication of the altar should be observed with gladness and joy for eight days, beginning with the twenty-fifth day of the month of Chislev.
There's a somewhat later (first century B.C.E.) account in 2 Maccabees 10:1-8 (again, RSV):
1: Now Maccabeus and his followers, the Lord leading them on, recovered the temple and the city;
2: and they tore down the altars which had been built in the public square by the foreigners, and also destroyed the sacred precincts.
3: They purified the sanctuary, and made another altar of sacrifice; then, striking fire out of flint, they offered sacrifices, after a lapse of two years, and they burned incense and lighted lamps and set out the bread of the Presence.
4: And when they had done this, they fell prostrate and besought the Lord that they might never again fall into such misfortunes, but that, if they should ever sin, they might be disciplined by him with forbearance and not be handed over to blasphemous and barbarous nations.
5: It happened that on the same day on which the sanctuary had been profaned by the foreigners, the purification of the sanctuary took place, that is, on the twenty-fifth day of the same month, which was Chislev.
6: And they celebrated it for eight days with rejoicing, in the manner of the feast of booths, remembering how not long before, during the feast of booths, they had been wandering in the mountains and caves like wild animals.
7: Therefore bearing ivy-wreathed wands and beautiful branches and also fronds of palm, they offered hymns of thanksgiving to him who had given success to the purifying of his own holy place.
8: They decreed by public ordinance and vote that the whole nation of the Jews should observe these days every year.
The story about the lamp that didn't run out of oil for eight days is found in the Babylonian Talmud, Shabbat 2 (p. 34):
What is 'Hanukah? The rabbis taught: "On the twenty-fifth day of Kislev 'Hanukah commences and lasts eight days, on which lamenting (in commemoration of the dead) and fasting are prohibited. When the Hellenists entered the sanctuary, they defiled all the oil that was found there. When the government of the House of Asmoneans prevailed and conquered them, oil was sought (to feed the holy lamp in the sanctuary) and only one vial was found with the seal of the high priest intact. The vial contained sufficient oil for one day only, but a miracle occurred, and it fed the holy lamp eight days in succession. These eight days were the following year established as days of good cheer, on which psalms of praise and acknowledgment (of God's wonders) were to be recited.
UPDATE: More here.