The single-layer cuprate superconductor HgBa₂CuO_(4+δ) (Hg1201) is an ideal candidate for investigating many properties of cuprates with minimal disorder and without the complication of multiple CuO₂ layers. Here we measure the in-plane longitudinal thermal conductivity κ of underdoped Hg1201 (T_c = 76 K, p = 0.11) at dilution refrigerator temperatures to extract the nodal quasiparticle velocity ratio v_F/v_Δ. Assuming contributions from only a single line node per quadrant on the Fermi surface leads to a value of v_F/v_Δ = 23 ± 3, anomalously large compared to other cuprates at similar dopings. In conjunction with the anomalously high quasiparticle specific heat of Hg1201 in the normal state reported previously at a similar doping, this points to more than one Fermi surface sheet crossing the nodal line, suggesting the presence of more than the single small electron pocket detected by quantum oscillations.