To investigate the critical thickness of ferroelectric BaTiO3 (BTO) films, we fabricated fully strained SrRuO3/BTO/SrRuO3 heterostructures on SrTiO3 substrates by pulsed laser deposition with in situ reflection high-energy electron diffraction. We varied the BTO layer thickness from 3 to 30 nm. By fabricating 10×10 mum2 capacitors, we could observe polarization versus electric-field hysteresis loops, which demonstrate the existence of ferroelectricity in BTO layers thicker than 5 nm. This observation provides an experimental upper bound of 5 nm for the critical thickness. The BTO thickness-dependent scaling of the remanent polarization agrees with the predictions of recent first-principle simulations [J. Junquera and P. Ghosez, Nature 422, 506 (2003)].