The El Niño-Southern Oscillation (ENSO) is the dominant mode of interannual climate variability with wide-ranging socio-economic and environmental impacts. Understanding the response of ENSO to a warmer climate is paramount, but many studies utilise different climate models which have their own physics and parameterisations. This can lead to the role of internal climate variability, that is, unforced natural variability, being underestimated. Using thirty-five Community Earth System Model Large Ensemble (CESM-LE) simulations, we examine the nonlinear ENSO relationship, its response to a warmer climate, and the influence of internal variability. Despite only small differences in round-off error and initial conditions, CESM-LE is able to generate a spread in ENSO amplitude and skewness that is similar to models participating in phase 5 of the Coupled Model Intercomparison Project (CMIP5). The spread of the projected change in amplitude and skewness is also similar between CMIP5 and CESM-LE, suggesting that internal climate variability may contribute to the projected ENSO response.