Disordered proteins play an essential role in a wide variety of biological processes, and are often posttranslationally modified. One such protein is histone H1; its highly disordered C-terminal tail (CH1) condenses internucleosomal linker DNA in chromatin in a way that is still poorly understood. Moreover, CH1 is phosphorylated in a cell cycle-dependent manner that correlates with changes in the chromatin condensation level. Here we present a model system that recapitulates key aspects of the in vivo process, and also allows a detailed structural and biophysical analysis of the stages before and after condensation. CH1 remains disordered in the DNA-bound state, despite its nanomolar affinity. Phase-separated droplets (coacervates) form, containing higher-order assemblies of CH1/DNA complexes. Phosphorylation at three serine residues, spaced along the length of the tail, has little effect on the local properties of the condensate. However, it dramatically alters higher-order structure in the coacervate and reduces partitioning to the coacervate phase. These observations show that disordered proteins can bind tightly to DNA without a disorder-to-order transition. Importantly, they also provide mechanistic insights into how higher-order structures can be exquisitely sensitive to perturbation by posttranslational modifications, thus broadening the repertoire of mechanisms that might regulate chromatin and other macromolecular assemblies.