AS RAZI points out, the first verse of this surah appears almost like a continuation of the last verses of the preceding one, especially 53: 57 - "that [Last Hour] which is so near draws ever nearer" -: and so we may assume that both were revealed at approximately the same time, i.e., towards the end of the early part (perhaps the fourth year) of Muhammad's prophethood.
THE LAST HOUR draws near, and the moon is I split asunder!1