Excitons in two-dimensional (2D) materials are tightly bound and exhibit rich physics. So far, the optical excitations in 2D semiconductors are dominated by Wannier-Mott excitons, but molecular systems can host Frenkel excitons (FE) with unique properties. Here, we report a strong optical response in a class of monolayer molecular J-aggregates. The exciton exhibits giant oscillator strength and absorption (over 30% for monolayer) at resonance, as well as photoluminescence quantum yield in the range of 60-100%. We observe evidence of superradiance (including increased oscillator strength, bathochromic shift, reduced linewidth and lifetime) at room-temperature and more progressively towards low temperature. These unique properties only exist in monolayer owing to the large unscreened dipole interactions and suppression of charge-transfer processes. Finally, we demonstrate light-emitting devices with the monolayer J-aggregate. The intrinsic device speed could be beyond 30 GHz, which is promising for next-generation ultrafast on-chip optical communications.