My rosary group desires to have eucharistic exposition while we pray the rosary. Is this allowed?
It is allowed to pray the rosary publicly during the eucharistic exposition. What’s not allowed is to expose the Eucharist for the main purpose of praying the rosary. The reason for this restriction is to make sure that pious exercises do not detract the faithful from the purpose of Eucharistic adoration. The Congregation for Divine Worship and the Discipline of the Sacraments, in the 34th edition of Notitiae (1998), expresses the following :
One should not expose the Eucharist only to recite the rosary. However, among the prayers that are used during adoration, the recitation of the rosary may certainly be included, emphasizing the Christological aspects with biblical readings relating to the mysteries, and providing time for silent adoration and meditation on them. (507-511). Also: “In the surroundings of exposition, anything must be carefully avoided that could in any way obscure Christ’s intention of instituting the Holy Eucharist above all in order to be near us to feed, to heal, and to comfort us” (Eucharisticum Mysterium 60 ).