  The timelike boundary Liouville (TBL) conformal field theory consisting of a
negative norm boson with an exponential boundary interaction is considered. TBL
and its close cousin, a positive norm boson with a non-hermitian boundary
interaction, arise in the description of the $c=1$ accumulation point of $c<1$
minimal models, as the worldsheet description of open string tachyon
condensation in string theory and in scaling limits of superconductors with
line defects. Bulk correlators are shown to be exactly soluble. In contrast,
due to OPE singularities near the boundary interaction, the computation of
boundary correlators is a challenging problem which we address but do not fully
solve. Analytic continuation from the known correlators of spatial boundary
Liouville to TBL encounters an infinite accumulation of poles and zeros. A
particular contour prescription is proposed which cancels the poles against the
zeros in the boundary correlator $d(\o) $ of two operators of weight $\o^2$ and
yields a finite result. A general relation is proposed between two-point CFT
correlators and stringy Bogolubov coefficients, according to which the
magnitude of $d(\o)$ determines the rate of open string pair creation during
tachyon condensation. The rate so obtained agrees at large $\o$ with a
minisuperspace analysis of previous work. It is suggested that the mathematical
ambiguity arising in the prescription for analytic continuation of the
correlators corresponds to the physical ambiguity in the choice of open string
modes and vacua in a time dependent background.
