We apply a low-frequency (mHz) ac pressure gradient to a sample of solid helium in order to search for a superfluidlike response. Our results are consistent with zero supersolid flow. Through a statistical analysis of our data, we set a bound on the rate of mass flow between two chambers, and hence the mass current density j. At the 68% confidence level, we bound v≡j/Ï≤9.6× 10-4 nm/s for the mass transport velocity. In terms of a simple model for the supersolid, we find an upper bound of 8.4× 10-6 for the supersolid fraction at 25 mK, at this same confidence level. These findings force the conclusion that the NCRI observed in the torsional oscillator experiments is not evidence for a frequency- independent superfluidlike state. Supersolid behavior is a frequency-dependent phenomenon, clearly evident at frequencies above 100 Hz of the torsional oscillator experiments, but undetectably small at frequencies approaching zero. © 2009 The American Physical Society.