  An analysis of Lyman series lines arising from hydrogen-like oxygen and neon
ions in the coronae of the active RS CVn-type binaries II Peg and IM Peg,
observed using the {\it Chandra} High Resolution Transmission Grating
Spectrograph, shows significant decrements in the Ly$\alpha$/Ly$\beta$ ratios
as compared with theoretical predictions and with the same ratios observed in
similar active binaries. We interpret these decrements in terms of resonance
scattering of line photons out of the line-of-sight; these observations present
the first strong evidence for this effect in active stellar coronae. The net
line photon loss implies a non-uniform and asymmetric surface distribution of
emitting structures on these stars. Escape probability arguments, together with
the observed line ratios and estimates of the emitting plasma density, imply
typical line-of-sight sizes of the coronal structures that dominate the X-ray
emission of $10^{10}$ cm at temperatures of $3\times 10^6$ K and of $10^8$ cm
at $10^7$ K. These sizes are an order of magnitude larger than predicted by
simple quasi-static coronal loops models, but are still very small compared to
the several $10^{11}$ cm radii of the underlying stars.
