  We study the chirality of ground-state alkali atoms in E and B fields,
dressed with a circularly-polarized laser beam close-detuned from an
E-field-assisted forbidden transition, such as 7S-8S in Fr. We predict a parity
violating energy shift of their sublevels, linear in E, and the weak nuclear
charge Q_W$. A dressing beam of 10 kW/cm$^2$ at 506 nm produces a shift of
$\sim100 \mu$Hz at E=100 V/cm, B $\gtrsim$30 mG. It should be observable with
$\sim 10^4$ Fr atoms confined in an optical dipole trap. We discuss optimal
conditions, parameter reversals and a calibration procedure to measure $Q_W$.
