The two-dimensional electron system in an InAs quantum well has emerged as a prime candidate for hosting exotic quasi-particles with non-Abelian statistics such as Majorana fermions and parafermions. To attain its full promise, however, the electron system has to be clean enough to exhibit electron-electron interaction phenomena. Here we report the observation of fractional quantum Hall effect in a very low disorder InAs quantum well with a well-width of 24 nm, containing a two-dimensional electron system with a density $n=7.8 times 10^{11}$ cm$^{-2}$ and low-temperature mobility $1.8 times 10^6$ cm$^2$/Vs. At a temperature of $simeq35$ mK and $Bsimeq24$ T, we observe a deep minimum in the longitudinal resistance, accompanied by a nearly quantized Hall plateau at Landau level filling factor $ u=4/3$.