Volcanic eruptions caused major weather and climatic changes on timescales ranging from hours to centuries in the past. Volcanic particles are injected in the atmosphere both as primary particles rapidly deposited due to their large sizes on time scales of minutes to a few weeks in the troposphere, and secondary particles mainly derived from the oxidation of sulfur dioxide. These particles are responsible for the atmospheric cooling observed at both regional and global scales following large volcanic eruptions. However, large condensational sinks due to preexisting particles within the plume, and unknown nucleation mechanisms under these circumstances make the assumption of new secondary particle formation still uncertain because the phenomenon has never been observed in a volcanic plume. In this work, we report the first observation of nucleation and new secondary particle formation events in a volcanic plume. These measurements were performed at the puy de Dôme atmospheric research station in central France during the Eyjafjallajokull volcano eruption in Spring 2010. We show that the nucleation is indeed linked to exceptionally high concentrations of sulfuric acid and present an unusual high particle formation rate. In addition we demonstrate that the binary H2SO4 - H2O nucleation scheme, as it is usually considered in modeling studies, underestimates by 7 to 8 orders of magnitude the observed particle formation rate and, therefore, should not be applied in tropospheric conditions. These results may help to revisit all past simulations of the impact of volcanic eruptions on climate.