The chromatin fiber is a complex of DNA and specific proteins called histones forming the first structural level of organization of eukaryotic chromosomes. In tightly organized chromatin fibers, the short segments of naked DNA linking the nucleosomes are strongly end constrained. Longitudinal thermal fluctuations in these linkers allow intercalative mode of protein binding. We show that mechanical constraints generated in the first stage of the binding process induce linker DNA buckling; buckling in turn modifies the binding energies and activation barriers and creates a force of decondensation at the chromatin fiber level. The unique structure and properties of DNA thus yield a novel physical mechanism of buckling instability that might play a key role in the regulation of gene expression.