  In the context of a recently proposed nonlinear massive gravity with
Lorentz-invariant mass terms, we investigate open Friedmann-Robertson-Walker
(FRW) universes driven by arbitrary matter source. While the flat FRW solutions
were recently shown to be absent, the proof does not extend to the open
universes. We find three independent branches of solutions to the equations of
motion for the St\"uckelberg scalars. One of the branches does not allow any
nontrivial FRW cosmologies, as in the previous no-go result. On the other hand,
both of the other two branches allow general open FRW universes governed by the
Friedmann equation with the matter source, the standard curvature term and an
effective cosmological constant $\Lambda_{\pm}=c_{\pm}m_g^2$. Here, $m_g$ is
the graviton mass, +and - represent the two branches, and $c_{\pm}$ are
constants determined by the two dimensionless parameters of the theory. Since
an open FRW universe with a sufficiently small curvature constant can
approximate a flat FRW universe but there is no exactly flat FRW solution, the
theory exhibits a discontinuity at the flat FRW limit.
