The online Style & Referencing guide - University Library homepage - includes examples of how to cite the Church conciliar documents of Vatican II (Second Vatican Council).
For the Chicago 'notes and bibliography' style, see the section of that guide covering 'Religious and classical works', i.e. :
Conciliar Documents - Second Vatican Council
First footnote citation
3. Second Vatican Council, “Lumen gentium
: Dogmatic Constitution on the Church” (hereafter LG) in The Documents of Vatican II,
ed. Walter M. Abbott (New York: Guild Press, 1966), 57.
Second and subsequent footnote citations
Second Vatican Council. “Lumen gentium: Dogmatic Constitution on the Church.” In The Documents of Vatican II. Edited by Walter M. Abbott. New York, NY: Guild Press, 1966.