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Below its Jahn--Teller transition temperature, \\(T_JT\\), NaNiO\\(_2\\) has a monoclinic layered structure consisting of alternating layers of edge-sharing NaO\\(_6\\) and Jahn-Teller-distorted NiO\\(_6\\) octahedra. Above \\(T_JT\\) where NaNiO\\(_2\\) is rhombohedral, diffraction measurements show the absence of a cooperative Jahn-Teller distortion, accompanied by an increase in the unit cell volume. Using neutron total scattering, solid-state Nuclear Magnetic Resonance (NMR), and extended X-ray absorption fine structure (EXAFS) experiments as local probes of the structure we find direct evidence for a displacive, as opposed to order-disorder Jahn-Teller transition at \\(T_JT\\). This is supported by ab initio molecular dynamics (AIMD) simulations. To our knowledge this study is the first to show a displacive Jahn-Teller transition in any material using direct observations with local probe techniques.