Adhesive silicone elastomer sheet afforded by the cure of a hydrosilylation-curing silicone elastomer composition comprising: (A) an organopolysiloxane that contains at least one diorganosiloxane unit and that has at least two silicon-bonded alkenyl groups in each molecule, (B) an organopolysiloxane resin with the average unit formula: (R13SiO1/2)x(SiO4/2)1.0 in which R1 is substituted or unsubstituted monovalent hydrocarbon group and x is a number from 0.5 to 1.0, (C) an organopolysiloxane that contains at least two silicon-bonded hydrogen atoms in each molecule, and (D) a hydrosilylation catalyst. The adhesive silicone elastomer sheet is transparent, and whose surface exhibits a stable and permanent adhesiveness.