Chanting could be written without time markings—as in most Byzantine notation—but that does not mean it has no rhythm or, furthermore, that within a singular chant tradition some things may be done in a freer rhythm than others (i.e. verses—stichoi—can begin in a free, logathes, rhythm only to end up with the rhythm of the sticheron they precede, also take the Doxa and Kai nyn of the first stasis of the anabathmoi for mode IV as used in festal Orthros services).
There is a great confusion as to rhythm in Byzantine chant and the interpretation of the great hypostaseis signs as interpreted by some western musicologists. Even with the New Method, there are good number of very good chanters who would not necessarily be able to correctly divide the pieces they chant into correct measures. As a by the way, there is an 1815 ms in the New Method of Petros Peloponesse's Anastasematarion in the Nat. Lib. of Greece (Metochion Panagiou Taphou 716) that has red 'measure' lines incorrectly dividing the music into four-beat measures. Anyway, rhythm is closely connected with each thesis as it relates to the particular genre it is being used with.
There are a large number of transcriptions of Byzantine Music into the western staff notation that use no time signatures or measures. These are usually done by people who do not know that there is rhythm in Byzantine chant or do not choose to believe so.