An n=7 Aurivillius phase, Sr4Bi4Ti7O24, with c=6.44 nm, was synthesized as an epitaxial (001)-oriented film. This phase and its purity were confirmed by x-ray diffraction and transmission electron microscopy. The material is ferroelectric, with a P-r=5.3 mu C/cm(2) oriented in the (001) plane and a paraelectric-to-ferroelectric transition temperature of T-C=324 K. Some indications of relaxorlike behavior are observed. Such behavior is out of character for Srn-1Bi2TinO3n+3 Aurivillius phases and is closer to the bulk behavior of doped SrTiO3, implying a spatial limit to the elastic interlayer interactions in these layered oxides. A finite-element solution to the interpretation of data from interdigitated capacitors on thin films is also described.