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We performed polarized reflection and transmission measurements on the layered conducting oxide PdCoO₂thin films. For theab-plane, an optical peak near Ω ≈ 750 cm⁻¹drives the scattering rate 1/τ(ω) and effective massm^*(ω) of the Drude carrier to increase and decrease respectively forω ≧ Ω. For thec-axis, a longitudinal optical phonon (LO) is present at Ω as evidenced by a peak in the loss function Im[−1/ε_c(ω)]. Further polarized measurements in different light propagation (q) and electric field (E) configurations indicate that the Peak at Ω results from an electron-phonon coupling of theab-plane carrier with thec-LO phonon, which leads to the frequency-dependent 1/τ(ω) andm^*(ω). This unusual interaction was previously reported in high-temperature superconductors (HTSC) between a non-Drude, mid-infrared (IR) band and ac-LO. On the contrary, it is the Drude carrier that couples in PdCoO₂. The coupling between theab-plane Drude carrier andc-LO suggests that thec-LO phonon may play a significant role in the characteristicab-plane electronic properties of PdCoO₂, including the ultra-high dc-conductivity, phonon-drag, and hydrodynamic electron transport.