There are many ways to begin introducing the chanted Propers into your parish's liturgical life, and it seems CMAA has been building something of a cottage industry devoted to exploring these possibilities.
Due to the cyclical and holistic nature of the Propers, and the aversion to treating Gregorian Chant as "just another option among many," there hasn't been (that I've noticed) much discussion about occasional use of the Propers. This is understandable, but there are times when, even in the context of a non-Propers-oriented program, one or more of the Proper chants are a particularly good fit, and could be introduced as a special choir piece. While this may run the risk of reinforcing Gregorian Chant as either "for special occasions" or "one more choice among many," I have to think it's better than never singing these pieces at all.
The Feast of the Ascension (tomorrow and/or this Sunday) seems to me to be one of those times where the text and the style of the chants from the Gradual Romanum seem to be a perfect fit, even in a conventional "contemporary" parish liturgical setting where the texts of the lessons provide the "theme" for musical selections.
The Ascension is an event in which the Apostles (and we with them) witness the marriage of Heaven and Earth as Jesus, in His living body, is lifted from this world to His Throne. The angels come to testify to this event, asking the twelve why they are standing there "looking at the sky." The earthy heavenliness of unaccompanied chant provides a particularly apt aural framework for experiencing this event in our present time. The otherworldliness of Chant, especially Chant in Latin, is evocative of the voice of the angels (especially since the Introit and optional Offertory are both the words of the Angels themselves).
Gregorian chant is unmetered, that is, there is no forward movement of rhythm (or of harmony, for that matter). The musical effect of this is that Chant feels set apart from Time- we do not experience the passage of time with Chant the way we do in metered music. This characteristic of Chant evokes the words of Jesus in the first reading, "It is not for you to know the times or seasons that the Father has established by his own authority."
Another characteristic of Chant, it's very nature as anonymously composed music of the Church (as opposed to music written by an identifiable individual) evokes the epistle's sanctuary not "built by human hands."
If you are of a mind to do some Chant, and have been trying to find a way to "work it in," Ascension might provide the perfect opportunity to try out a little Chant in your community, and gauge its reception.