I will discuss the super-horizon (iso)curvature perturbations arising from statistical fluctuations during a first-order phase transition (FOPT). Finite statistics in various Hubble patches during an FOPT result in perturbations that follow a generic power-law scaling in FOPT parameters. Even if the FOPT occurs in a secluded dark sector, the resulting curvature perturbation is constrained by cosmological data. Utilizing Cosmic Microwave Background and Large Scale Structure measurements, I present the primary constraint on energy released in a dark-sector FOPT, expressed as a ratio of dark to Standard Model radiation. For cosmological FOPTs between photon temperatures of 0.1 eV to 1 keV, this constraint already surpasses the ∆Neff bound typically cited for PT in a dark sector. Future constraints on the primordial curvature perturbation may further extend the bound to the 100 MeV scale.