Plant viruses are submitted to narrow population bottlenecks both during infection of their hosts and during horizontal transmission between host individuals. The size of bottlenecks exerted on virus populations during plant invasion has been estimated in a few pathosystems but is not addressed yet for horizontal transmission. Using competition for aphid transmission between two Potato virus Y variants, one of them being noninfectious but equally transmissible, we obtained estimates of the size of bottlenecks exerted on an insect-borne virus during its horizontal transmission. We found that an aphid transmitted on average 0.5–3.2 virus particles, which is extremely low compared with the census viral population into a plant. Such narrow bottlenecks emphasize the strength of stochastic events acting on virus populations, and we illustrate, in modeling virus emergence, why estimating this parameter is important.