  We calculate the subleading corrections to the thrust rate using
Soft-Collinear Effective Theory to factorize the rate and match onto jet and
soft operators that describe the degrees of freedom of the relevant scales. We
work in the perturbative regime where all the scales are well above
\Lambda_QCD. The thrust rate involves an incomplete sum over final states that
is enforced by a measurement operator. Subleading corrections require matching
onto not only the higher dimensional dijet operators, but also matching onto
subleading measurement operators in the effective theory. We explicitly show
how to factorize the O(\alpha_s \tau) thrust rate into a hard function
multiplied by the convolution of the vacuum expectation value of jet and soft
operators. Our approach can be generalized to other jet shapes and rates.
