We investigate the presence of logarithmic CFT doublets in the soft sector of
celestial CFT related with supertranslations. We show that the quantum operator
associated with a $\log u$ late-time behavior for the asymptotic gravitational
shear forms a logarithmic CFT pair of conformal dimension $\Delta=1$ with an
IR-regulated supertranslation Goldstone current. We discuss this result in
connection with previous encounters of log CFT structures in the IR-finite part
of celestial OPEs.
