VERITAS Observations of the Unusual Extragalactic Transient Swift J164449.3+573451

We report on very-high-energy ($>$100 GeV) gamma-ray observations of Swift J164449.3+573451, an unusual transient object first detected by the {\it Swift} Observatory and later detected by multiple radio, optical and X-ray observatories. A total exposure of 28 hours was obtained on Swift J164449.3+573451 with VERITAS during 2011 March 28 -- April 15. We do not detect the source and place a differential upper limit on the emission at 500 GeV during these observations of $1.4 \times 10^{-12}$ erg cm$^{-2}$ s$^{-1}$ (99% confidence level). We also present time-resolved upper limits and use a flux limit averaged over the X-ray flaring period to constrain various emission scenarios that can accommodate both the radio-through-X-ray emission detected from the source and the lack of detection by VERITAS.