Homogeneous, isotropic mediums characterized by relative permittivity scalars ε = ε _R + iε _I\, (ε_R, ε_I ∈ \bb R) and relative permeability scalars μ = μ_R + iμ_I\, (μ_R, μ_I ∈ \bb R) are well known to support the propagation of plane waves with negative phase velocity (NPV), provided that both [?]R < 0 and mR < 0. We demonstrate that mediums which do not support NPV propagation when viewed at rest (e.g., mediums with [?]R > 0 and mR > 0), can support NPV propagation when they are viewed in a reference frame which is uniformly translated at a sufficiently high velocity. Representative numerical examples are used to explore the constitutive parameter regimes which support NPV propagation under the uniform-velocity condition.