A new excitation is observed at 201 meV in the doped-hole ladder cuprate Sr$_{14}$Cu$_{24}$O$_{41}$, using ultraviolet resonance Raman scattering with incident light at 3.7 eV polarized along the direction of the rungs. The excitation is found to be of charge nature, with a temperature independent excitation energy, and can be understood via an intra-ladder pair-breaking process. The intensity tracks closely the order parameter of the charge density wave in the ladder (CDW$_L$), but persists above the CDW$_L$ transition temperature ($T_{CDW_L}$), indicating a strong local pairing above $T_{CDW_L}$. The 201 meV excitation vanishes in La$_{6}$Ca$_{8}$Cu$_{24}$O$_{41+delta}$, and La$_{5}$Ca$_{9}$Cu$_{24}$O$_{41}$ which are samples with no holes in the ladders. Our results suggest that the doped holes in the ladder are composite bosons consisting of paired holons that order below $T_{CDW}$.
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