  We obtain a new interpretation of the cohomological Hall algebra
$\mathcal{H}_Q$ of a symmetric quiver $Q$ in the context of the theory of
vertex algebras. Namely, we show that the graded dual of $\mathcal{H}_Q$ is
naturally identified with the underlying vector space of the principal free
vertex algebra associated to the Euler form of $Q$. Properties of that vertex
algebra are shown to account for the key results about $\mathcal{H}_Q$. In
particular, it has a natural structure of a vertex bialgebra, leading to a new
interpretation of the product of $\mathcal{H}_Q$. Moreover, it is isomorphic to
the universal enveloping vertex algebra of a certain vertex Lie algebra, which
leads to a new interpretation of Donaldson--Thomas invariants of $Q$ (and, in
particular, re-proves their positivity). Finally, it is possible to use that
vertex algebra to give a new interpretation of CoHA modules made of
cohomologies of non-commutative Hilbert schemes.
