Summary: For an arbitrary differential graded algebra \(A\) with finite-dimensional total cohomology we introduce a pairing on the Hochschild homology of \(A\), derive an explicit formula for the Chern characters of perfect \(A\)-modules (the Chern characters take values in the Hochschild homology of \(A\)), and prove a Hirzebruch-Riemann-Roch-type formula which expresses the Euler characteristic of the Hom-complex between two perfect \(A\)-modules in terms of the pairing of their Chern characters.