  We consider the 4-dimensional $\mathcal{N}=1$ Lie superconformal algebra and
search for completely "symmetric" (in the graded sense) 3-index invariant
tensors. The solution we find is unique and we show that the corresponding
invariant polynomial cubic in the generalized curvatures of superconformal
gravity vanishes. Consequently, the associated Chern-Simons polynomial is a
non-trivial anomaly cocycle. We explicitly compute this cocycle to all orders
in the independent fields of superconformal gravity and establish that it is
BRST equivalent to the so-called superconformal $a$-anomaly. We briefly discuss
the possibility that the superconformal $c$-anomaly also admits a similar
Chern-Simons formulation and the potential holographic, 5-dimensional,
interpretation of our results.
