Our latest results have just been accepted for publication in Nature Communications. In this work we strongly couple the exciton of cyanine dye J-aggregates to an optical mode of a Fabry-Perot (FP) cavity, and achieve an enhancement of the complex nonlinear refractive index by two orders of magnitude compared with that of the uncoupled condition. Moreover, the coupled system shows an ultrafast response of ~120 fs that we extract from optical cross-correlation measurements. The ultrafast and large enhancement of the optical nonlinar coefficients in this work paves the way for exploring strong coupling effects on various third-order nonlinear optical phenomena and for technological application. The paper is now accessible in Open Access on Nature Communications website and on our publications page.