We present high-resolution observations of CH3CN (J = 6-5), (CO)-O-18 (J = 1-0), and 2.7 mm continuum toward a region of massive star formation in the G9.62+0.19 H II region complex. Our observations reveal three embedded centers of massive star formation located along the major axis of an elongated molecular cloud core. Two of those (components D and F) are observed close to the maximum of (CO)-O-18 column density, whereas component E is located at the edge of the molecular core. Based on the (CO)-O-18 observations, we derive cloud core dimensions of 0.6 x 0.3 pc, a total mass of 1000 M(.), and a mean hydrogen density of 2 x 10(5) cm(-3) for an assumed temperature of 30 K. The cloud core has a systematic velocity gradient of 9 km s(-1) pc(-1) along its major axis. The embedded centers of massive star formation are all detected in the 2.7 mm continuum, and all three are bright, compact sources of CH3CN (J = 6-5) emission. Component D is an ultracompact (UC) H II region with an electron density of 1.8 x 10(5) cm(-3), an electron temperature of 8000 K, a diameter less than or equal to 0.014 pc, and an ionizing star of type B0.5 zero-age main sequence (ZAMS). For component E, the power-law spectrum of index 1.1 between 2 cm and 2.7 mm, together with the small angular diameter, suggests that the continuum emission is produced either by a partially ionized stellar wind or by an UC H II region of electron density 8.0 x 10(5) cm(-3) and a diameter less than or equal to 0.0025 pc, ionized by a star of type B1 ZAMS, plus some excess dust emission. Our (CO)-O-18 and 2.7 mm continuum data indicate that the mass associated with component E is in the range 122-160 M(.). For component F, continuum emission is only detected at 2.7 mm. It is likely that most or all of this emission is produced by warm circumstellar dust. If so, then we estimate a total mass associated with component F of 55-160 M(.), depending on the temperature of the gas and dust, which is not well determined for this object. Broad line wings in the (CO)-O-18 line are detected close to the position of component F; we interpret this is as being due to a bipolar molecular how. Thus, component F is probably a pre-main-sequence star which may still be in a rapid accretion phase, and we postulate that it is the youngest of the three centers of massive star formation in the G9.62+0.19 cloud core. In fact, it may be one of the youngest massive stars yet identified. Each of the continuum components D, E, and F are enclosed in very compact, dense, warm molecular cocoons. Analysis of our CH3CN and (CO)-O-18 data indicates gas temperatures in the range 50 K (component D) to possibly as high as 300 K (component F), but more likely similar to 100 K (components E and F). The optical depths in the lower K-transitions of CH3CN (J = 6-5) are greater than unity toward all three sources. From our large velocity gradient analysis, we obtain methyl cyanide column densities in the range 5 x 10(15) cm(-2) (component D) to 1 x 10(17) cm(-2) (component F); the methyl cyanide abundance is clearly enhanced at least in component F and probably also in components D and E. Hydrogen densities are in excess of 10(7) cm(-3) in components E and F. The systematic increase in density, column density, and temperature in components D, E, and F, respectively, together with properties of the continuum emission at the three positions, leads us to suggest that components D-F probably represent an evolutionary sequence, with component D being the oldest and component F being the youngest among the three centers of massive star formation.