Ultrathin crystalline films offer the possibility of exploring phase transitions in the crossover region between two and three dimensions. Second-order ferromagnetic phase transitions have been observed in monolayer magnetic films(1,2), where surface anisotropy energy stabilizes the two-dimensional ferromagnetic state at finite temperature(3). Similarly, a number of magnetic materials have magnetic surface layers that show a second-order ferromagnetic-paramagnetic phase transition with an increased Curie temperature(4). Ferroelectricity is in many ways analogous to ferromagnetism, and bulk-like ferroelectricity and finite-size modifications of it have been seen in nanocrystals as small as 250 Angstrom in diameter(5), in perovskite films 100 Angstrom thick(6) and in crystalline ferroelectric polymers as thin as 25 Angstrom (refs 7-10). But these results can be interpreted as bulk ferroelectricity suppressed by surface depolarization energies, and imply that the bulk transition has a minimum critical size(11-13). Here we report measurements of the ferroelectric transition in crystalline films of a random copolymer of vinylidene fluoride and trifluoroethylene just 10 Angstrom (two monolayers) thick. We see a first-order ferroelectric phase transition with a transition temperature nearly equal to the bulk value, even in these almost two-dimensional films. In addition, we see a second first-order transition at a lower temperature, which seems to be associated with the surface layers only. The near-absence of finite-size effects on the bulk transition implies that these films must be considered as two-dimensional ferroelectrics.