We have studied the fluoride-bridged Dy-Cr molecular nanomagnet [Dy(hfac)(4)-CrF2(py)(4)]center dot 1/2CHCl(3) by x-ray magnetic circular dichroism (XMCD). The obtained element-specific magnetization curves allow for a quantification of the sign and strength of the magnetic exchange coupling between the Dy and the Cr ions. In an effective spin-1/2 formalism only taking into account the ground Kramers doublet of the Dy-III ion, we find a coupling strength of j (eff,z) = -2.3(1) cm(-1). Further, we find that the ground Kramers doublet is nearly perfectly axial with g (eff,z) ,D-y = 19.6(6) and g (eff,xy) ,D-y = 0(2). The coupling value corresponds to a "true", non-effective isotropic coupling of j = -0.16 cm(-1) when taking into account a full J = 15/2 angular momentum. This coupling strength is comparable to that of j = -0.18 cm(-1) previously found in the related fluoride-bridged compound Dy-Cr-Dy.