A resonant-tunneling conductivity was experimentally registered in a doped heterostructure with a single quantum well using admittance spectroscopy. Earlier, this effect was only realized in artificially created resonant tunneling structures, having four heterojunctions. A heterostructure with an In0.3Ga0.7As/GaAs quantum well was examined in the temperature range of 10–300 K. In admittance spectra, a competition of thermionic and tunneling escape mechanisms was noticed with a non-exponential Arrhenius plot. By means of numerical self-consistent simulations in a quantum box, we have shown the role of a quasi-bound level in resonant tunneling of electrons; in addition, the energies and wave functions of the quasi-bound state were derived in dependence on an applied bias. The modification of a transparency coefficient for a two-barrier Hartree potential as a function of the quantum well width and in dependence on the applied bias was also calculated. The resonant state took place only at symmetric barriers and disappeared, when the electric field tilted the barriers. The results can be used to develop a new type of resonant tunneling diodes and as a method for diagnostics of the tunnel effect in semiconductors.