  In nuclear matter, the pion weak decay constant is separated into the two
components $f_t, f_s$ corresponding to the time and space components of the
axial-vector current. Using QCD sum rules, we compute the two decay constants
from the pseudoscalar-axial vector correlation function in the matter $i \int
d^4x~ e^{ip\cdot x} < \rho| T[{\bar d}(x) i \gamma_5 u (x)~ {\bar u}(0)
\gamma_\mu \gamma_5 d (0)] | \rho>$. It is found that the sum rule for $f_t$
satisfies the in-medium Gell-Mann--Oakes--Renner (GOR) relation precisely while
the $f_s$ sum rule does not. The $f_s$ sum rule contains the non-negligible
contribution from the dimension 5 condensate $<{\bar q} i D_0 iD_0 q >_N +
{1\over 8} < {\bar q} g_s \sigma \cdot {\cal G} q >_N$ in addition to the
in-medium quark condensate. Using standard set of QCD parameters and ignoring
the in-medium change of the pion mass, we obtain $f_t =105$ MeV at the nuclear
saturation density. The prediction for $f_s$ depends on values of the dimension
5 condensate and on the Borel mass. However, the OPE constrains that $f_s/f_t
\ge 1 $, which does not agree with the prediction from the in-medium chiral
perturbation theory. Depending on the value of the dimension 5 condensate,
$f_s$ at the saturation density is found to be in the range $ 112 \sim 134$ MeV
at the Borel mass $M^2 \sim 1$ GeV$^2$.
