[[Image:UNA.png|right]]According to the United Noahide Academies forum, Rabbi Schochet says: Noahide men (or women) should not buy their own tallis gadol to use during their daily morning prayers, or a tallis katan to wear continually (even with the tzitzis fringes not showing). The tallis is a uniquely Jewish symbol. Thus a Noahide who wears a tallis is likely to be mistaken for a Jew in a synagogue service or in other settings (including the places where a Noahide might go without hesitation, but which would be forbidden for an observant Jew to be seen there).
Also, if a tzitzis fringe on a Noahide's tallis came undone on the end and he retied it himself, it would be forbidden for a Jew to put on that tallis, since it would no longer be fulfilling the mitzvah, and thus the four-corned garment would be forbidden for him to wear. This is one reason why a Noahide should not have his own tallis, because it might get acquired or borrowed by a Jew.