The Kali-Santāraṇa Upaniṣad (कलिसन्तरन) is a Vaiṣṇava Vedantic text associated with the Kṛṣṇa Yajurveda. It is the source of the "Hare Kṛṣṇa" mantra, explaining that "These sixteen words are destructive of the evil effects of Kali Yuga." In the Muktikā canon of 108 Upanishads, it is counted as number 103.
The Upaniṣad asserts that whoever recites the mantra 35 million (sardha trikotir) times will be absolved from the sin of the murder of a Brahmin, the theft of gold, sexual intercourse with a woman of a lower caste, or even generally from any sin altogether. With a daily quota of 16 rosaries with 108 beads (1.5 hours of chanting), this count would be reached in 55.5 years.
The Upaniṣad at least predates the 16th century when the mantra was popularized by Chaitanya Mahaprabhu, and is believed to be of ancient origin by his followers (Gauḍiya Vaiṣṇavism).
Here is the English translation of the Upaniṣad Text:
Hari Oṃ ! At the end of Dvāpara Yuga, Nārada went to Brahma and addressed him thus: "O Lord, how shall I, roaming over the earth, be able to across Kali ?"
To which Brahma thus replied: "Well asked. Hearken to that which all Śrutis (the Vedas) keep secret and hidden, through which one may cross the Saṃsāra (mundane existence) of Kali. He shakes off (the evil effects of) Kali through the mere uttering of the name of the Lord Nārāyaṇa, who is the primeval Puruṣa".
Again Nārada asked Brahma: "What is the name ?" To which Hiraṇyagarbha (Brahma) replied thus:
1. Hare Rāma Hare Rāma Rāma Rāma Hare Hare Hare Kṛṣṇa Hare Kṛṣṇa Kṛṣṇa Kṛṣṇa Hare Hare
2. These sixteen names (words) are destructive of the evil effects of Kali. No better means than this is to be seen in all the Vedas.
These (sixteen names) destroy the Avaraṇa (or the centripetal force which produces the sense of individuality) of Jīva surrounded by the sixteen Kala-s (rays). Then like the sphere of the sun which shines fully after the clouds (screening it) disperse, Parābrahman (alone) shines."
Nārada asked: ‘O Lord, what are the rules to be observed with reference to it ?" To which Brahma replied that there were no rules for it. Whoever in a pure or an impure state, utters these always, attains the same world of, or proximity with, or the same form of, or absorption into Brahma.
Whoever utters three and a half Crores (or thirty-five millions) times this Mantra composed of sixteen names (or words) crosses the sin of the murder of a Brāhmaṇa. He becomes purified from the sin of the theft of gold. He becomes purified from the sin of cohabitation with a woman of low caste. He is purified from the sins of wrong done to Pitṛ-s, Deva-s and men. Having given up all Dharma-s, he becomes freed at once from all sins. He is at once released from all bondage. That he is at once released from all bondage is the Upaniṣad.
Hari Oṃ Tat Sat !