The authors show that CaF2:Y crystals that have been X-irradiated at low temperatures contain Y2+ ions associated with a trigonally located interstitial F- ion. Experimental results are presented that support this identification and that show that a trigonal Jahn-Teller effect (with warping) is involved. An estimate for the Jahn-Teller energy of EJT approximately=490 cm-1 is obtained.