  The paper is an attempt to resolve the prescribed Chern scalar curvature
problem. We look for solutions within the conformal class of a fixed Hermitian
metric. We divide the problem in three cases, according to the sign of the
Gauduchon degree, that we analyse separately. In the case where the Gauduchon
degree is negative, we prove that every non-identically zero and non-positive
function is the Chern scalar curvature of a unique metric conformal to the
fixed one. Moreover, if there exists a balanced metric with zero Chern scalar
curvature, we prove that every smooth function changing sign with negative mean
value is the Chern scalar curvature of a metric conformal to the balanced one.

Differential Geometry;Complex Variables