  We derive a factorization theorem for production of an arbitrary number of
color-singlet particles accompanied by a fixed number of jets at the LHC. The
jets are defined with the standard anti-$k_T$ algorithm, and the fixed number
of jets is obtained by imposing a veto on additional radiation in the final
state. The formalism presented here is useful for current Higgs boson analyses
using exclusive jet bins, and for other studies using a similar strategy. The
derivation uses the soft-collinear effective theory and assumes that the
transverse momenta of the hard jets are larger than the veto scale. We resum
the large Sudakov logarithms $\alpha_s^n \log^{2n-m}(p_T^{J}/p_T^{veto})$ up to
the next-to-leading-logarithmic accuracy, and present numerical results for
Higgs boson production in association with a jet at the LHC. We comment on the
experimentally-interesting parameter region in which we expect our
factorization formula to hold.
