We investigate tunneling through a resonant level embedded in a dissipative environment, which suppresses tunneling rates at low temperatures. Specifically, the resonant level is formed in a carbon nanotube quantum dot, and the dissipative environment is realized by fabricating resistive leads. For the symmetric coupling of the resonant level to the two leads, we find that the resonant peak reaches the unitary conductance e^2/h despite the presence of dissipative modes. Simultaneously, the width of the resonance tends to zero as a non-trivial power of temperature. We draw a connection between our system and a resonant tunneling in a Luttinger liquid and interpret the observed unitary resonance of vanishing width in terms of a quantum critical point (QCP). We further investigate an exotic state of electronic matter obtained by fine-tuning the system exactly to the QCP. We report on several transport scaling laws both near and far from equilibrium, including a non-Fermi-liquid quasi-linear scattering rate at the QCP, interpreted in terms of a Majorana mode localized at the resonant level.