X-ray disk winds are detected in spectrally soft, disk-dominated phases of stellar-mass black hole outbursts. In contrast, compact, steady, relativistic jets are detected in spectrally hard states that are dominated by non-thermal X-ray emission. Although these distinctive outflows appear to be almost mutually exclusive, it is possible that a disk wind persists in hard states but cannot be detected via X-ray absorption lines owing to very high ionization. Here, we present an analysis of a deep, 60 ksec Chandra/HETGS observation of the black hole candidate H 1743-322 in the low/hard state. The spectrum shows no evidence of a disk wind, with tight limits, and within the range of ionizing flux levels that were measured in prior Chandra observations wherein a wind was clearly detected. In H 1743-322, at least, disk winds are actually diminished in the low/hard state, and disk winds and jets are likely state-dependent and anti-correlated. These results suggest that although the launching radii of winds and jets may differ by orders of magnitude, they may both be tied to a fundamental property of the inner accretion flow, such as the mass accretion rate and/or the magnetic field topology of the disk. We discuss these results in the context of disk winds and jets in other stellar-mass black holes, and possible launching mechanisms for black hole outflows.