We present a catalog of 840 X-ray sources and first results from a 100 ks Chandra X-ray Observatory imaging study of the filamentary infrared dark cloud G014.225$-$00.506, which forms the central regions of a larger cloud complex known as the M17 southwest extension (M17 SWex). In addition to the rich population of protostars and young stellar objects with dusty circumstellar disks revealed by Spitzer Space Telescope archival data, we discover a population of X-ray-emitting, intermediate-mass pre--main-sequence stars (IMPS) that lack infrared excess emission from circumstellar disks. We model the infrared spectral energy distributions of this source population to measure its mass function and place new constraints on the inner dust disk destruction timescales for 2-8 $M_{odot}$ stars. We also place a lower limit on the star formation rate (SFR) and find that it is quite high ($dot{M}ge 0.007~M_{odot}$ yr$^{-1}$), equivalent to several Orion Nebula Clusters in G14.225$-$0.506 alone, and likely accelerating. The cloud complex has not produced a population of massive, O-type stars commensurate with its SFR. This absence of very massive (${ge}20~M_{odot}$) stars suggests that either (1) M17 SWex is an example of a distributed mode of star formation that will produce a large OB association dominated by intermediate-mass stars but relatively few massive clusters, or (2) the massive cores are still in the process of accreting sufficient mass to form massive clusters hosting O stars.
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