  We have measured the Stark shift of the $A^2\Pi_{1/2} - X^2\Sigma^+$
transition in YbF. We use a molecular beam triple resonance method, with two
laser transitions acting as pump and probe, assisted by an rf transition that
tags a single hyperfine transition of the X state. After subtracting the known
ground state Stark shift, we obtain a value of $70.3(1.5) $Hz/(V/cm)$^2$ for
the static electric polarizability of the state $A^2\Pi_{1/2}(J=1/2,f)$. From
this we calculate a value $\mu_e=2.46(3)$D for the electric dipole moment of
the $A^2\Pi_{1/2}(v=0)$ state.
