A freestanding thin film of n-tetracontane chains is simulated by a Monte Carlo (MC) method on a high coordination lattice. The coarse-grained chains, represented by 20 beads each, can be reverse-mapped into the fully atomistic description, C40H82. The Hamiltonian includes a short-range interaction based on a rotational isomeric state model and a long-range interaction obtained from a Lennard-Jones potential energy function. When the melt is instantaneously quenched from 473 to 298 K, crystallization initiates in the surface region and propagates into the interior of the film, as was found in a prior molecular dynamics simulation of a united atom model of polyethylene [M. Ito, M. Matsumoto, and M. Doi, Fluid Phase Equilibria, 144, 395 (1998)]. Several repetitions of the MC simulation, starting from different configurations of the melt at 473 K, reveal that two distinctly different structures can be obtained. Usually the independently initiated crystals at the two surfaces of the thin film produce a disordered grain boundary when they impinge on one another as a consequence of propagation into the interior of the film. This grain boundary was also observed by Ito However, if the MC simulation is repeated many times, there are a few instances in which the independently initiated crystals happen to have a similar orientation, and then crystallization propagates completely through the thin film without producing a grain boundary in the interior. A well-defined melting phenomenon is observed at about 390 K when the film without the grain boundary is heated. Annealing at 380 K of the film with the grain boundary causes growth of one crystal at the expense of the other. This growth eventually leads to a completely crystalline film, with elimination of the grain boundary. Therefore, the stable structure of the thin film is the one that is completely crystalline, with no grain boundary in the interior, even though rapid quenching is more likely to lead to a structure with a grain boundary. The MC simulation can anneal the imperfect structure into the more perfect one.