Liouville field theory has long been a cornerstone of two-dimensional quantum field theory and quantum gravity, which has attracted much recent attention in the mathematics literature. Timelike (or imaginary) Liouville field theory is a version of Liouville field theory where the coupling constant is made imaginary. I will talk about recent work that gives a rigorous construction of timelike Liouville theory in a restricted regime of parameters. The path integral for timelike Liouville field theory has a negative sign in front of the kinetic term, which makes it closer to a theory of quantum gravity than the usual (spacelike) Liouville field theory. Making sense of this "wrong sign" requires a theory of Gaussian random variables with negative variance. I will present such a theory, which will then be used to prove the timelike DOZZ formula for the 3-point correlation function in the restricted region. Expressions are derived also for the k-point correlation functions will also be presented, and I will show how these functions approach the correct semiclassical limits after insertion of heavy vertex operators.