What is perhaps most telling is that no one gives the full source for this "quotation." Most web writers simply call the source "Chilam Balam" without noting that the title denotes 14 separate books. No one gives the specific volume cited (the Chilam Balam of Tizimin, the Chilam Balam of Chumayel, etc.), so there is no way to find out which this refers to.
If a Google Books search can be believed (and this isn't always the case with their weird new algorithm that sometimes returns results lacking the search terms), the first mention of this fake quote came from 1970's Not of This World by Peter Kolosimo. The author, however, had a still different "translation": "Creatures arriving from the sky on flying ships ... white gods who fly above the spheres and reach the stars." This is the English version. Kolosimo wrote in Italian, where the line is rendered «Esseri scesi dal cielo su navi volanti... dèi bianchi che volano su cerchi e toccano le stelle».
That line doesn't appear in any Chilam Balam texts I have access to either. I checked Kolosimo's text in the original Italian and found that he gave no source for his "quotation." We should simply accept it on his word. The Italian text of the alleged quotation does not appear in any indexed book, so it seems that it was not a standard Italian translation of any book of Chilam Balam that Kolosimo used.
Kolosimo was an Italian author, the Italian Erich von Daniken, whose Not of This World won Italy's highest literary prize. Nevertheless, what we seem to have in this case is a modern paraphrase of a 1970 English translation of an Italian translation of a Spanish translation of the Maya original--or maybe Kolosimo just making stuff up. There's really no way to know. And we know how well it worked out when Pauwels and Bergier tried it with the Mahabharata. At so far a remove from the original source, no wonder Kolosimo and his followers could make it say pretty much anything.