In the older form of the Divine Office, using the Roman Breviary of 1960, there is an additional office, Prime. From its name one can see it is the prayer recited at the first hour of daytime. A feature of this office is the reading of the Roman Martyrology entry for the day, and on December 24, it is the announcement of the birth of Christ.
Vatican II specifically called for Prime to be suppressed, meaning that the reading of the martyrology is lost every day, and I think it's especially lost on Christmas, since we have quite a wonderful text to work with. Should Prime have been deleted? It dates to the early Western church, but an ecumenical council said to do so, unfortunately with no explanation. Really, I'm curious. Out of all things, what had happened to Prime that required its suppression? One should keep in mind that the laity would never have heard this chant prior to the council unless in a monastery or religious house, considering that Prime is a minor hour, firstly, and secondly the Divine Office was not encouraged as it is today.
That being said, it would be nice if this officially was to precede, in everywhere and place, and not just by local decision in accordance with yet another option, the Mass of Christmas during the Night. The text has changed in the new martyrology, but I suppose one could use either text if sung before the Mass in the older form.