  We calculate penguin contributions to the lifetime splitting between the B_s
and the B_d meson. In the Standard Model the penguin effects are found to be
opposite in sign, but of similar magnitude as the contributions of the
current-current operators, despite of the smallness of the penguin
coefficients. We predict
  tau(B_s)/tau(B_d) -1 = ( -1.2 +/- 10.0 ) * 10^(-3) * (f_{B_s}/190 MeV)^2
where the error stems from hadronic uncertainties. Since penguin coefficients
are sensitive to new physics and poorly tested experimentally, we analyze the
possibility to extract them from a future precision measurement of
tau(B_s)/tau(B_d). Anticipating progress in the determination of the hadronic
parameters epsilon_1, epsilon_2 and f_{B_s}/f_{B_d} we find that the
coefficient C_4 can be extracted with an uncertainty of order |Delta C_4|= 0.1
from the double ratio (tau(B_s)-tau(B_d))/(tau(B^+)-tau(B_d)), if
|epsilon_1-epsilon_2| is not too small.
