Highly relativistic jets are a key element of current gamma-ray burst models, where the jet kinetic energy is converted to radiation energy at optically thin shocks. High-energy neutrinos are also expected, from interactions of protons accelerated in the same shocks. Here we revisit the early evolution of a relativistic jet, while the jet is still inside the star, and investigate its neutrino emission. In particular we study propagation of mildly relativistic and ultrarelativistic jets through a type Ib progenitor, and follow reverse shocks as the jets cross the star. We show that protons can be accelerated to 10(4)-10(5) GeV at reverse shocks, and efficiently produce mesons. The mesons experience significant cooling, suppressing subsequent neutrino emission. We show, however, that the neutrino yield from the reverse shock is still reasonably large, especially for low-luminosity and long-duration jets, where meson cooling is less severe. We discuss implications of our results in the context of neutrinos from choked jets, which are completely shock heated and do not break out of the star. From a choked jet with isotropic equivalent energy of 1053 erg at 10 Mpc, we expect similar to 20 neutrino events at IceCube.