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Kronos was the offspring of a forbidden union, that had been made unlawful by the Ancient Covenant, of a Chronovore, Prometheus, and the Eternal who was known as Elektra. (The Quantum Archangel) He had described himself as “beyond good and evil”.
At the moment of his conception, Kronos had been trapped in a crystal, and had been cast down to the Ephemeral universe. Eventually, the crystal would land on the planet of the Constructors of Destiny, where he influenced their culture and became a godlike figure to them. Kronos continued to have this effect on other planets and culture he encountered, including the Dæmons. The Dæmons then sent the crystal to Atlantis on Earth, so it could destroy it, because the Dæmons deemed it a failed experiment. (The Quantum Archangel)
In the 1970s, the Master had used a crystal named after Kronos on Earth, to cause him to manifest so that (he thought) he might bind Kronos to his will. This failed and the Master went back in time to the last days of Atlantis. Kronos ruined the city. In the aftermath, he stopped both the Doctor’s and the Master’s TARDIS in the Time Vortex and, appearing as a huge, translucent female face, asked the Third Doctor whether he wanted Kronos to destroy the Master. The Doctor demurred, Kronos let him free, and the Master vanished into his TARDIS. (The Time Monster)
During the Quantum Archangel crisis, Kronos had created the persona of Paul Kairos, was a student under Ruth Ingram and Stuart Hyde, to manifest upon the Earth. Kairos, through miraculous talent, had reverse-engineered the Master‘s TOMTIT device, and had created an enhanced version, the TITAN Array. He was refused the rights to his own invention, the quantum lattice, by Anjeliqua Whitefriar, and was in a relationship with a fellow student, Arlene Cole.
As Kairos, he had worked with the Sixth Doctor and helped end the crisis by shedding his human guise and attacking the Mad Mind of Bophemeral during a violent engagement between the Archangel and the Doctor. Following this, he had allowed the Kairos persona to remain active as an independent being, but was not before Kronos was forced to sacrifice his life in order to destroy the Mad Mind. (TThe Quantum Archangel)