  We introduce a higher rank analog of the Pandharipande-Thomas theory of
stable pairs on a Calabi-Yau threefold $X$. More precisely, we develop a moduli
theory for frozen triples given by the data $O^r(-n)\rightarrow F$ where $F$ is
a sheaf of pure dimension 1. The moduli space of such objects does not
naturally determine an enumerative theory: that is, it does not naturally
possess a perfect symmetric obstruction theory. Instead, we build a
zero-dimensional virtual fundamental class by hand, by truncating a
deformation-obstruction theory coming from the moduli of objects in the derived
category of $X$. This yields the first deformation-theoretic construction of a
higher-rank enumerative theory for Calabi-Yau threefolds. We calculate this
enumerative theory for local $\mathbb{P}^1$ using the Graber-Pandharipande
virtual localization technique.
