  We argue that the celestial conformal field theory exhibits patterns of a
logarithmic conformal field theory. We uncover a Jordan block structure
involving the celestial stress tensor and its logarithmic partner, a composite
operator built from the stress tensor and the Liouville field. Using a limiting
process whose parameter corresponds to the infrared cut-off of gravity, we
perform some basic consistency checks, particularly the calculation of
two-point correlators, which reveals the expected logarithmic behavior. We
comment on the vanishing value of the central charge in the celestial conformal
field theory and explain how the logarithmic partner is relevant for its
well-behavedness.
