  We define Jacobi forms with complex multiplication. Analogous to modular
forms with complex multiplication, they are constructed from Hecke characters
of the associated imaginary quadratic field. From this construction we obtain a
Jacobi form which specializes to $\eta(\tau)^{26}$ which we present to
highlight an open question of Dyson and Serre. We give other examples and
applications of Jacobi forms with complex multiplication including constructing
theta blocks associated to elliptic curves with complex multiplication and new
families of congruences and cranks for certain partition functions.
