Explosive dynamical events in controlled-nuclear-fusion devices (known as edge-localized modes) display many similarities to solar-flare events on the sun, revealing a new connection between laboratory plasma physics and astronomy. However, to date there has been no direct evidence for the peeling mode structure, due to the lack of decisive diagnostics. Here we report the first evidence for the structure and dynamical steady state of a peeling mode for low-n edge-harmonic oscillations (EHOs) in the quiescent H-mode. EHOs are dominated by the fundamental mode (1fEHO) at both the low- and high-field sides. 1fEHO edge perturbations are confirmed to have kink parity and exhibit the frozen-in-condition predicted by a linear stability analysis. The envelope signal of the 1fEHO mode exhibits repeated cycles of growth and damping to the order of a few hundred Hz associated with small changes in an edge gradient, and results are quantitatively consistent with a limit-cycle-oscillation model.