  Drinfeld Zastava is a certain closure of the moduli space of maps from the
projective line to the Kashiwara flag scheme of the affine Lie algebra
$\hat{sl}_n$. We introduce an affine, reduced, irreducible, normal quiver
variety $Z$ which maps to the Zastava space bijectively at the level of complex
points. The natural Poisson structure on the Zastava space can be described on
$Z$ in terms of Hamiltonian reduction of a certain Poisson subvariety of the
dual space of a (nonsemisimple) Lie algebra. The quantum Hamiltonian reduction
of the corresponding quotient of its universal enveloping algebra produces a
quantization $Y$ of the coordinate ring of $Z$. The same quantization was
obtained in the finite (as opposed to the affine) case generically in
arXiv:math/0409031. We prove that, for generic values of quantization
parameters, $Y$ is a quotient of the affine Borel Yangian.
