  We construct Euclidean Liouville conformal field theories in odd number of
dimensions. The theories are nonlocal and non-unitary with a log-correlated
Liouville field, a ${\cal Q}$-curvature background, and an exponential
Liouville-type potential. We study the classical and quantum properties of
these theories including the finite entanglement entropy part of the sphere
partition function $F$, the boundary conformal anomaly and vertex operators'
correlation functions. We derive the analogue of the even-dimensional DOZZ
formula and its semi-classical approximation.
