Measurement of the thermoviscoelastic behavior of glass-forming liquids in the nanometer size range offers the possibility of increased understanding of the fundamental nature of the glass-transition phenomenon itself. We present results from use of a previously unknown method for characterizing the theological response of nanometer-thick polymer films. The method relies on the imaging capabilities of the atomic force microscope and the reduction in size of the classical bubble inflation method of measuring the biaxial creep response of ultrathin polymer films. Creep compliance as a function of time and temperature was measured in the linear viscoelastic regime for films of poly(vinyl acetate) at a thickness of 27.5 nanometers. Although little evidence for a change in the glass temperature is found, the material exhibits previously unobserved stiffening in the rubbery response regime.