In the Kali-santarana-upanisad, the Hare Krishna mahamantra is given in that way. But to say that the name of Rama must precede the name of Krishna in the mantra is a superficial understanding. It is said that because it comes from the Upanisads, the Hare Krishna mantra is a Vedic mantra, and therefore, because the ordinary people may not have any entrance into Vedic mantras, Sri Chaitanya Mahaprabhu readjusted this mantra by reversing the order of the words. In that way, it is said, the concern that it is a Vedic mantra is thereby canceled, and so Sri Chaitanya Mahaprabhu gave it to all without breaching the injunctions of the Vedas. Some devotees in Uttar Pradesh, who have great affection for Sri Chaitanyadev, like to give this opinion.
But our faith is that the mentioning of Hare Rama first is only superficial. It concerns the idea that since the Rama-avatar appeared first and the Krishna-avatar afterwards, the name of Rama, Hare Rama, should come first in the mahamantra. A deeper reading will consider that when two similar things are connected together, the priority will be ordered not on the basis of historical precedent, but in consideration of the most highly developed conception. The Holy Name of Krishna is higher than the Holy Name of Rama. This is mentioned in the Puranas: three names of Rama equal one name of Krishna. The name of Krishna is superior to the name of Rama. Where the two are connected together, the first position should be given to the one that is superior. Therefore, the name of Krishna must come first in the mahamantra.
This is one point. Another point is that within the eternal plane, everything is moving in a cyclic order. In an eternal cycle, which is first and which is next cannot be ascertained, and so, in the eternal plane of lila, it cannot be determined whether Krishna is before Rama or Rama is before Krishna. So, from that consideration also, since the Names of Krishna and Rama are eternal and unrelated to any historical event, we may begin the mantra from any place.