  We introduce a basis of the symmetric functions that evaluates to the
(irreducible) characters of the symmetric group, just as the Schur functions
evaluate to the irreducible characters of $GL_n$ modules. Our main result gives
three different characterizations for this basis. One of the characterizations
shows that the structure coefficients for the (outer) product of these
functions are the stable Kronecker coefficients. The results in this paper
focus on developing the fundamental properties of this basis.
