The Planckian relaxation rate $\ensuremath{\hbar}/{t}_{\mathrm{P}}=2\ensuremath{\pi}{k}_{\mathrm{B}}T$ sets a characteristic timescale for both the equilibration of quantum critical systems and maximal quantum chaos. In this Rapid Communication, we show that at the critical coupling between a superconducting dot and the complex Sachdev-Ye-Kitaev model, known to be maximally chaotic, the pairing gap $\mathrm{\ensuremath{\Delta}}$ behaves as $\ensuremath{\eta}\phantom{\rule{0.16em}{0ex}}\ensuremath{\hbar}/{t}_{\mathrm{P}}$ at low temperatures, where $\ensuremath{\eta}$ is an order one constant. The lower critical temperature emerges with a further increase of the coupling strength so that the finite $\mathrm{\ensuremath{\Delta}}$ domain is settled between the two critical temperatures.