  Double-polarization observables in the reaction $\vec{e}p \rightarrow
e'\vec{p'}\gamma{}$ have been measured at $Q^2=0.33 (GeV/c)^2$. The experiment
was performed at the spectrometer setup of the A1 Collaboration using the 855
MeV polarized electron beam provided by the Mainz Microtron (MAMI) and a recoil
proton polarimeter. From the double-polarization observables the structure
function $P_{LT}^\perp$ is extracted for the first time, with the value $(-15.4
\pm 3.3 (stat.)^{+1.5}_{-2.4} (syst.)) GeV^{-2}$, using the low-energy theorem
for Virtual Compton Sattering. This structure function provides a hitherto
unmeasured linear combination of the generalized polarizabilities of the
proton.
