We describe a Chandra X-ray Target of Opportunity project designed to isolate the site of TeV flaring in the radio galaxy M87. To date, we have triggered the Chandra observations only once (2010 April) and by the time of the first of our 9 observations, the TeV flare had ended. However, we found that the X-ray intensity of the unresolved nucleus was at an elevated level for our first observation. Of the more than 60 Chandra observations we have made of the M87 jet covering 9 years, the nucleus was measured at a comparably high level only 3 times. Two of these occasions can be associated with TeV flaring, and at the time of the third event, there were no TeV monitoring activities. From the rapidity of the intensity drop of the nucleus, we infer that the size of the emitting region is of order a few light days x the unknown beaming factor; comparable to the same sort of estimate for the TeV emitting region. We also find evidence of spectral evolution in the X-ray band which seems consistent with radiative losses affecting the non-thermal population of the emitting electrons within the unresolved nucleus. Show Partial Abstract