Local polar distortions, their collective ordering, and their field-driven reversal have been studied extensively in ferroelectric perovskites for decades. Here we identify an unusual behavior in the ferroelectric halide perovskite CsGeBr3 using large-scale molecular dynamics with first-principles-trained interatomic potentials. In its nominally cubic phase the Ge off-centering forms one-dimensional polar chains that extend over at least tens of nanometers and relax on nanosecond timescales, four orders of magnitude slower than in BaTiO3 and PbTiO3, with CsSnBr3 in between. The cubic CsGeBr3 phase is a dynamically disordered state in which oppositely polarized chains flip throughout the crystal, and a long-lived one-dimensional local polarization coexists with zero net polarization. A simple three-dimensional perovskite thus hosts long-ranged one-dimensional polar correlations with remarkably slow dynamics. In the ferroelectric phase the same chains set a one-dimensional switching mechanism, in which the polarization reverses chain by chain.