Many modelling studies suggest that the El Niño-Southern Oscillation (ENSO), in interaction with the tropical Pacific background climate, will change with rising atmospheric greenhouse gas concentrations. Solar geoengineering (reducing the solar flux from outer space) has been proposed as a means to counteract anthropogenic climate change. However, the effectiveness of solar geoengineering concerning a variety of aspects of Earth's climate is uncertain. Robust results are particularly challenging to obtain for ENSO because existing geoengineering simulations are too short (typically ∼ 50 years) to detect statistically significant changes in the highly variable tropical Pacific background climate. We here present results from a 1000-year-long solar-geoengineering simulation, G1, carried out with the coupled atmosphere-ocean general circulation model HadCM3L. In agreement with previous studies, reducing the solar irradiance (4 %) to offset global mean surface warming in the model more than compensates the warming in the tropical Pacific that develops in the 4 × CO2 scenario. We see an overcooling of 0.3 °C and a 0.23 mm d-1 (5 %) reduction in mean rainfall over the tropical Pacific relative to preindustrial conditions in the G1 simulation, owing to the different latitudinal distributions of the shortwave (solar) and longwave (CO2) forcings. The location of the Intertropical Convergence Zone (ITCZ) in the tropical Pacific, which moved 7.5° southwards under 4 × CO2, is restored to its preindustrial position. However, other aspects of the tropical Pacific mean climate are not reset as effectively. Relative to preindustrial conditions, in G1 the time-averaged zonal wind stress, zonal sea surface temperature (SST) gradient, and meridional SST gradient are each statistically significantly reduced by around 10 %, and the Pacific Walker Circulation (PWC) is consistently weakened, resulting in conditions conducive to increased frequency of El Niño events. The overall amplitude of ENSO strengthens by 9 %-10 % in G1, but there is a 65 % reduction in the asymmetry between cold and warm events: cold events intensify more than warm events. Notably, the frequency of extreme El Niño and La Niña events increases by ca. 60 % and 30 %, respectively, while the total number of El Niño events increases by around 10 %. All of these changes are statistically significant at either 95 or 99 % confidence level. Somewhat paradoxically, while the number of total and extreme events increases, the extreme El Niño events become weaker relative to the preindustrial state, while the extreme La Niña events become even stronger. That is, such extreme El Niño events in G1 become less intense than under preindustrial conditions but also more frequent. In contrast, extreme La Niña events become stronger in G1, which is in agreement with the general overcooling of the tropical Pacific in G1 relative to preindustrial conditions.