The field of miniature mechanical oscillators is rapidly evolving, with emerging applications including signal processing, biological detection1 and fundamental tests of quantum mechanics2. As the dimensions of a mechanical oscillator shrink to the molecular scale, such as in a carbon nanotube resonator3–7, their vibrations become increasingly coupled and strongly interacting8,9 until even weak thermal fluctuations could make the oscillator nonlinear10–13. The mechanics at this scale possesses rich dynamics, unexplored because an efficient way of detecting the motion in real time is lacking. Here we directly measure the thermal vibrations of a carbon nanotube in real time using a high-finesse micrometre-scale silicon nitride optical cavity as a sensitive photonic microscope. With the high displacement sensitivity of 700 fm Hz−1/2 and the fine time resolution of this technique, we were able to discover a realm of dynamics undetected by previous time-averaged measurements and a room-temperature coherence that is nearly three orders of magnitude longer than previously reported. We find that the discrepancy in the coherence stems from long-time non-equilibrium dynamics, analogous to the Fermi–Pasta–Ulam–Tsingou recurrence seen in nonlinear systems14. Our data unveil the emergence of a weakly chaotic mechanical breather15, in which vibrational energy is recurrently shared among several resonance modes—dynamics that we are able to reproduce using a simple numerical model. These experiments open up the study of nonlinear mechanical systems in the Brownian limit (that is, when a system is driven solely by thermal fluctuations) and present an integrated, sensitive, high-bandwidth nanophotonic interface for carbon nanotube resonators. © 2019, Springer Nature Limited.