There is a feature that allows this; Reaction Fire. It can be toggled on and off, as well as allow multiple shots. If I remember correctly, I believe the default key is "x" or you can click on the small icon in the lower panel somewhat toward the left. (Sorry I don't have a screenshot handy at this moment.)
I think this feature is available in the 2.1 release as well as the beta - which version are you playing?
EDIT: Even when Reaction fire is enabled, there is still a chance a soldier might not be quick enough to act before an alien does, so there is still some risk and chance involved.