Intertwining intrinsic topological order with gapless collective modes remains a central challenge in many-body physics. We show that a quantum-Hall at ${\nu }_1={\nu }_2={\nu }_3=\frac{1}{3}$, tuned solely by the inter-layer spacing $d$, realizes this goal. Large-scale density-matrix renormalization group (DMRG) calculations and a Chern-Simons field theory analysis reveal an intermediate "anyon-exciton condensate" separating the familiar ${\nu }_{tot}=1$ exciton condensate ($d\to 0$) from three decoupled Laughlin liquids ($d\to \infty$). In this phase, neutral bi-excitons condense while a $\nu =\frac{2}{3}$ Laughlin topological order survives, yielding a Goldstone mode coexisting with fractionalized anyons. A Ginzburg-Landau analysis maps out the finite-temperature phase diagram. The anyon-exciton condensate can be experimentally verified through a vanishing double-counter-flow resistance and a fractional layer-resolved Hall resistance (R_{xy}= h/e^{2}), both within reach of existing high-mobility trilayer devices.