We study the influence of low-frequency current noise on a single-mode semiconductor laser subject to external optical feedback. We experimentally show that the addition of current noise modifies the power spectrum of the chaotic intensity fluctuations of the laser subject to feedback. From the power spectrum measurements, we can deduce interactions among the feedback-induced dynamics and the current noise. Numerical modeling based on Lang-Kobayashi rate equations provides additional insight, as the phase of the electric field can be analyzed. We find that the noise affects the coherence of the chaotic oscillations, thereby being able to alter their characteristics significantly as long as this coherence exists.