A leading-twist factorization formula is derived for the longitudinal structure function in the x -->1 limit of deeply inelastic scattering. This is achieved by defining a new jet function which is gauge independent and probes the transverse momentum of the struck parton in the target. In moment space, terms of order (ln^k N)/N, which are the leading ones for F_L, are shown to be resummable through the cusp anomalous dimension gamma_K and the anomalous dimension gamma_{J^prime} of the new jet function. This anomalous dimension is computed to O(alpha_s). The suggested factorization for F_L reproduces the fixed order results known to O(alpha_s^2). The general ideas for resumming the terms of order (ln^k N)/N in moment space may be extended to the other structure functions and to other inclusive processes near the elastic limit.
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