  We search for signatures of a distant planet around the two-million-year-old
classical T-Tauri star CI Tau hosting a hot Jupiter candidate (M_{p} sin{i} ~
8.1 M_{Jupiter}) in an eccentric orbit (e ~0.3). To probe the existence of an
outer perturber, we reanalyzed 1.3 mm dust continuum observations of the
protoplanetary disk around CI Tau obtained by the Atacama Large
Millimeter/submillimeter Array. We found a gap structure at ~0".8 in CI Tau's
disk. Our visibility fitting assuming an axisymmetric surface brightness
profile suggested that the gap is located at a deprojected radius of
104.5+/-1.6 au and has a width of 36.9+/-2.9 au. The brightness temperature
around the gap was calculated to be ~2.3 K lower than that of the ambient disk.
Gap-opening mechanisms such as secular gravitational instability and dust
trapping can explain the gap morphology in the CI Tau disk. The scenario that
an unseen planet created the observed gap structure cannot be ruled out,
although the coexistence of an eccentric hot Jupiter and a distant planet
around the young CI Tau would be challenging for gravitational scattering
scenarios. The mass of the planet was estimated to be between ~0.25 M_{Jupiter}
and ~0.8 M_{Jupiter} from the gap width and depth (0.41 +0.04/-0.06) in the
modeled surface brightness image, which is lower than the current detection
limits of high-contrast direct imaging. The young classical T-Tauri CI Tau may
be a unique system to explore the existence of a potential distant planet as
well as the origin of an eccentric hot Jupiter.
