We report the discovery of low-amplitude, short-period, multiperiodic luminosity variations in the hot B subdwarf PG 0014+ 067. This star was selected as a potential target in the course of our ongoing survey to search for pulsators of the EC 14026 type. Our model atmosphere analysis of the time-averaged Multiple Mirror Telescope (MMT) optical spectrum of PG 0014+ 067 indicates that this star has T eff= 33,550±380 K and log g= 5.77±0.10, which places it right in the middle of the theoretical EC 14026 instability region in the log g–T eff plane. A standard analysis of our Canada-France-Hawaii Telescope (CFHT) light curve reveals the presence of at least 13 distinct harmonic oscillations with periods in the range 80–170 s. Fine structure (closely spaced frequency doublets) is observed in three of these oscillations, and five high-frequency peaks due to nonlinear cross frequency superpositions of the basic oscillations are also possibly seen in the Fourier spectrum. The largest oscillation has an amplitude≃ 0.22% of the mean brightness of the star, making PG 0014+ 067 the EC 14026 star with the smallest intrinsic amplitudes so far. On the basis of the 13 observed periods, we carry out a detailed asteroseismological analysis of the data starting with an extensive search in parameter space for a model that could account for the observations. To make this search efficient, objective, and reliable, we use a newly developed period matching technique based on an optimization algorithm. This search leads to a model that can account remarkably well for the 13 observed periods in the light curve of PG 0014+ 067. A detailed comparison of the theoretical period spectrum of this optimal model with the distribution of the 13 observed periods leads to the realization that 10 other pulsations, with lower amplitudes than the threshold value used in our standard analysis, are probably present in the light curve of PG 0014+ 067. Altogether, we tentatively identify 23 distinct pulsation modes in our target star (counting the frequency doublets referred to above as single modes). These are all low-order acoustic modes with adjacent values of k and with l= 0, 1, 2, and 3. They define a band of unstable periods, in close agreement with nonadiabatic pulsation theory. Furthermore, the average relative dispersion between the 23 observed periods and the periods of the corresponding 23 theoretical modes of the optimal model is only≃ 0.8%, a remarkable achievement by asteroseismological standards. On the basis of our analysis, we infer that the global structural parameters of PG 0014+ 067 are log g= 5.780±0.008, T eff= 34,500 K±2690 K, M*/M⊙= 0.490±0.019, log (M env/M*)=-4.31±0.22, and R/R⊙= 0.149±0.004. If we combine these estimates of the surface gravity, total mass, and radius with our value of the spectroscopic temperature (which is more accurately evaluated than its asteroseismological counterpart, in direct contrast to the surface gravity), we also find that PG 0014+ 067 has a luminosity L/L⊙= 25.5±2.5, has an absolute visual magnitude M V= 4.48±0.12, and is located at a distance d= 1925±195 pc (using V= 15.9±0.1). If we interpret the fine structure (frequency doublets) observed in three of the 23 pulsations in terms of rotational splitting, we further find that PG 0014+ 067 rotates with a period of 29.2±0.9 hr and has a maximum rotational broadening velocity of V sin i≲ 6.2±0.4 km s-1.