  We study a controlled large-$N$ theory of electrons coupled to dynamical
two-level systems (TLSs) via spatially-random interactions. Such a physical
situation arises when electrons scatter off low-energy excitations in a
metallic glass, such as a charge or stripe glass. Our theory is governed by a
non-Gaussian saddle point, which maps to the celebrated spin-boson model. By
tuning the coupling strength we find that the model crosses over from a Fermi
liquid at weak coupling to an extended region of non-Fermi liquid behavior at
strong coupling, and realizes a marginal Fermi liquid at the crossover. Beyond
a critical coupling strength, the TLSs freeze and Fermi-liquid behavior is
restored. Our results are valid for generic space dimensions $d>1$.
