Linker histones such as H1 are abundant basic proteins that bind tightly to nucleosomes, thereby acting as key organizers of chromatin structure. The molecular details of linker histone interactions with the nucleosome, and in particular the contributions of linker DNA and of the basic C-terminal tail of H1, are controversial. Here we combine rigorous solution-state binding assays with native gel electrophoresis and Atomic Force Microscopy, to quantify the interaction of H1 with chromatin. We find that H1 binds nucleosomes and nucleosomal arrays with very tight affinity by recognizing a specific DNA geometry minimally consisting of a solitary nucleosome with a single ~18 base pair DNA linker arm. The association of H1 alters the conformation of trinucleosomes so that only one H1 can bind to the two available linker DNA regions. Neither incorporation of the histone variant H2A.Z, nor the presence of neighboring nucleosomes affects H1 affinity. Our data provide a comprehensive thermodynamic framework for this ubiquitous chromatin architectural protein.