We present an experiment to measure the delay upon reflection from a frustrated Gires-Tournois interferometer.  It has been predicted [1] that the time delay for a reflected pulse in this geometry should be negative. In experiments on absorption or tunneling, pulse reshaping ensures that energy transport on average never violates causality.  However, in this experiment the reflection amplitude is 100%.  We explore this apparent paradox while clarifying the relationship between the phenomenon and the Goos-Hanchen shift.  We measure the negative group delay time with a Hong-Ou-Mandel Interferometer, which offers sub-femtosecond time resolution and some dispersion cancellation effects. Experimental results are presented as well as a theoretical explanation of the apparent paradox.  [1] P. Tournois, IEEE J. Quantum Elect. 33, 1, (1997).