I think you may be confusing fugues and canons. With fugues, the thematic motive is usually the same from voice to voice for the first couple of measures, but after that the counterpoint develops differently in different voices. What you describe, the same melody throughout, would be a canon, where the melody is imitated exactly in the different voices (although at different pitch levels). Two that spring to mind: one is the four-voice "In te Domine speravi" of Hassler, and the other is the 24-voice "Qui habitat" by Josquin Desprez. Both are canonic, rather than fugal.

As for chant, yes, there is such a thing as chant done in canon. You have to pick very carefully but some that do work are Adoro te devote, veni veni emmanuel, and I have heard dies irae performed somewhat canonically.
In my improvisations I try to play the chants as canons occasionally and those three have been ones I have managed to do with some success.

So, nothing strictly fugal, but only canonic?

The lines among canon, fugue, and imitative counterpoint can be rather blurred ones at times. Certainly Palestrina and Josquin, as well as other Renaissance composers engaged in both imitative counterpoint and canon writing that, in some cases, could be called fugal, complete with successive entrances of a subject with departing lines after a certain point to account for the harmonic and other contrapuntal structure.

And sometimes this was done with a subject taken from chant. One nice example is how Palestrina treats the chant melody in his alternatim setting of "A solus ortis cardine" ... the voices enter in quick succession, similar to those in a canon, but the effect is still rather fugal in structure, thanks to the successive verses and their interpretations,

http://www.cpdl.org/wiki/images/d/dd/Palestrina-A_solis_ortus_cardine.mp3

Bach motets anyone?

Did he write any in Latin?

Jes says, '...somewhat canonically...'

I should imagine that the 'key word' here is 'somewhat'!
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It is important to remember that both canon and fugue are procedures, they are not, like sonata allegro form (if we consent to count 'sonata' a form rather than a family of forms), rondo, binary, ternary (if strict ternary exists) etc., 'forms'. Another 'form' that is a 'procedure' and not a 'form' would be chaconne or passacaglia. Another would be theme and variations. Canon is, by definition, the (usually) 'strict' imitation of the entire subject, or melodic progression, at one or more specified intervals, whereas fugue may or may not employ strict imitation, but varies even that with subject development and the possible introduction of ancillary themes, and secondary sections (episodes) with their own subject matter. Canons have a pedigree that reaches into the late mediaeval era. Fugal procedure developed, as Salieri noted, from the renaissance ricercar (there is a direct line from Frescobaldi et al., to Buxtehude et al., to Bach) and has not been surpassed since Bach spoke with infallible and final authority on the matter.

A canonic or fugal subject must inherently lend itself to any or all the following forms of imitation: strict, harmonic or modal, inversion, stretto, diminution, augmentation, retrograde, etc. Such a 'subject' would be, I think, very difficult to find in our chant repertory. Perhaps one could use just a snipet, or an incipit, of a given chant as a fugal subject. Some hymn tunes work in canon, most don't (though the Lutherans are more talented than others at daring canonical treatment of hymn tunes that others would shrink from - and!, their entire congregations sing them heartily).