  We analyze the possible existence of a pulsational instability excited by the
$\epsilon$-mechanism during the last few centuries of evolution of a
Chandrasekhar mass white dwarf prior to its explosion as a Type Ia supernova.
Our analysis is motivated by the temperature sensitivity of the nuclear energy
generation rate ($\sim T^{23}$) in a white dwarf whose structural adiabatic
index is near 4/3. Based upon a linear stability analysis, we find that the
fundamental mode and higher order radial modes are indeed unstable and that the
fundamental mode has the shortest growth time scale. However, the growth time
scale for such instability never becomes shorter than the evolutionary
timescale. Therefore, even though the star \emph{is} pulsationally unstable, we
do not expect these radial modes to have time to grow and to affect the
structure and explosion properties of Type Ia supernovae.
