  We compute the off-shell 1-loop tadpole amplitude in heterotic string field
theory. With a special choice of cubic vertex, we show that this amplitude can
be computed exactly. We obtain explicit and elementary expressions for the
Feynman graph decomposition of the moduli space, the local coordinate map at
the puncture as a function of the modulus, and the $b$-ghost insertions needed
for the integration measure. Recently developed homotopy algebra methods
provide a consistent configuration of picture changing operators. We discuss
the consequences of spurious poles for the choice of picture changing
operators.
