  The bound state of a $\tau^+\tau^-$ pair by the electromagnetic force is the
heaviest and smallest QED atom. Since the discovery of the two lightest QED
atoms more than 60 years ago, no evidence for the third one has been found. We
demonstrate that the $J_\tau$ ($\tau^+\tau^-$ atom with $J^{PC}=1^{--}$)
resonance signal can be observed with a significance larger than $5\sigma$
including both statistical and systematic uncertainties, via the process
$e^+e^-\to X^+ Y^- \slashed{E}$ ($X,\,Y=e$, $\mu$, $\pi$, $K$, or $\rho$, and
$\slashed{E}$ is the missing energy) with $1.5~{\rm ab^{-1}}$ data taken around
the $\tau$ pair production threshold. The $\tau$ lepton mass can be measured in
a precision of 2 keV with the same data sample. This is within one year's
running time of the proposed super tau-charm factory or super charm-tau
factory.
