  Light is one of the most powerful and precise tools allowing us to control,
shape and create new phases of matter. In this task, the magnetic component of
a light wave has so far played a unique role in defining the wave's helicity,
but its influence on the optical response of matter is weak. Chiral molecules
offer a typical example where the weakness of magnetic interactions hampers our
ability to control the strength of their chiral optical response. It is limited
several orders of magnitude below the full potential. Here we introduce freely
propagating locally and globally chiral electric fields, which interact with
chiral quantum systems extremely efficiently. To demonstrate the degree of
control enabled by such fields, we focus on the nonlinear optical response of
randomly oriented chiral molecules. We show full control over intensity,
polarization and propagation direction of the chiral optical response, enabling
its background-free detection. This response can be fully suppressed or
enhanced at will depending on the molecular handedness, achieving the ultimate
limit in chiral discrimination. Our findings open a way to extremely efficient
control of chiral matter and to ultrafast imaging of chiral structure and
dynamics in gases, liquids and solids.
