Republican candidates often receive between 30% and 40% of the two-way vote share in statewide elections in Massachusetts. For the last three Census cycles, Massachusetts has held 9–10 seats in the House of Representatives, which means that a district can be won with as little as six percent of the statewide vote. Putting these two facts together, it is striking that a Massachusetts Republican has not won a seat in the U.S. House of Representatives since 1994. We argue that the underperformance of Republicans in Massachusetts is not attributable to gerrymandering, nor to the failure of Republicans to field House candidates, but is a structural mathematical feature of the actual distribution of votes observable in some recent elections. Several of these elections have a remarkable property in their vote patterns: Republican votes clear 30%, but are distributed so uniformly that they are locked out of the possibility of representation. Though there are more ways of building a valid districting plan than there are particles in the galaxy, every single one of them would produce a 9–0 Democratic delegation.