  A locally compact group $G$ has the factorization property if the map
$$C^*(G)\odot C^*(G)\ni a\otimes b\mapsto \lambda(a)\rho(b)\in\mathcal
B(L^2(G))$$ is continuous with respect to the minimal C*-norm. This paper seeks
to initiate a rigorous study of this property in the case of locally compact
groups which, in contrast to the discrete case, has been relatively untouched.
A partial solution to the question of when the factorization property passes to
continuous embeddings is given -- a question which traces back to Kirchberg's
seminal work on the topic and is known to be false in general. It is also shown
that every "residually amenably embeddable" group must necessarily have the
factorization property and that an analogue of Kirchberg's characterization of
the factorization property for discrete groups with property (T) holds for a
more general class of groups.
