Single photons from semiconductor quantum dots are promising resources for linear optical quantum computing, or, when coupled to spin states, quantum repeaters. To realize such schemes, the photons must exhibit a high degree of indistinguishability. However, the solid-state environment presents inherent obstacles for this requirement as intrinsic semiconductor fluctuations can destroy the photon indistinguishability. Here, we demonstrate that resonant excitation of a quantum dot with a narrow-band laser generates near transform limited power spectra and indistinguishable photons from a single quantum dot in an environment with many charge-fluctuating traps. The specificity of the resonant excitation suppresses the excited state population in the quantum dot when it is detuned due to spectral fluctuations. The dynamics of this process lead to flickering of the emission over long time scales (>5 μs) and reduces the time-averaged count rates. Nevertheless, in spite of significant spectral fluctuations, high visibility two-photon interference can be achieved. This approach is useful for quantum dots with nearby surface states in processed photonic structures and quantum emitters in emerging platforms, such as two-dimensional semiconductors.