In small bowl, mix cream cheese and hot sauce until smooth. Mix in chicken and shredded cheese just until combined.
Unroll both cans of dough; separate into 8 triangles. On ungreased large cookie sheet, arrange triangles in ring so short sides of triangles form a 5-inch circle in center. (Dough will overlap; half of each triangle will hang over edges of cookie sheet. Dough ring should look like a sun.).
Spoon cream cheese mixture on the half of each triangle closest to center of ring. Top with blue cheese crumbles.
Bring each dough triangle hanging over side of pan up over filling, tucking dough under bottom layer of dough to secure it. Repeat around ring until entire filling is enclosed (some filling might show a little).
Gently separate dough perforations on top until filling peeks through.
Bake 20 to 25 minutes or until dough is golden brown and thoroughly baked. Cool 5 to 10 minutes before cutting into serving slices.