Dynamic optical coherence elastography (OCE) techniques have rapidly emerged as a noninvasive way to characterize the biomechanical properties of tissue. However, clinical applications of the majority of these techniques have been unfeasible due to the extended acquisition time because of multiple temporal OCT acquisitions (M-B mode). Moreover, multiple excitations, large datasets, and prolonged laser exposure prohibit their translation to the clinic, where patient discomfort and safety are critical criteria. Here, we demonstrate the feasibility of noncontact true kilohertz frame-rate dynamic optical coherence elastography by directly imaging a focused air-pulse induced elastic wave with a home-built phase-sensitive OCE system. The OCE system was based on a 4X buffered Fourier Domain Mode Locked swept source laser with an A-scan rate of ~1.5 MHz, and imaged the elastic wave propagation at a frame rate of ~7.3 kHz. Because the elastic wave directly imaged, only a single excitation was utilized for one line scan measurement. Rather than acquiring multiple temporal scans at successive spatial locations as with previous techniques, here, successive B-scans were acquired over the measurement region (B-M mode). Preliminary measurements were taken on tissue-mimicking agar phantoms of various concentrations, and the results showed good agreement with uniaxial mechanical compression testing. Then, the elasticity of an in situ porcine cornea in the whole eye-globe configuration at various intraocular pressures was measured. The results showed that this technique can acquire a depth-resolved elastogram in milliseconds. Furthermore, the ultra-fast acquisition ensured that the laser safety exposure limit for the cornea was not exceeded.