UPDATE: According to this page of a Dell Communities thread on this issue, Dell has officially acknowledged the issue and (as of this writing) is working on a fix. Here is also twitter thread about this issue.
Many users have noticed an unexpected sound emanating from their laptops, often loudest on the left side of the keyboard or by the USB ports along the left side of the laptop. It is most commonly labeled "coil whine," though it is unclear what exactly is responsible for the sound. Several users have noted that the sound changes in pitch and/or volume based on CPU/GPU load, but does not necessarily mean that those components are generating the noise themselves. The "coil whine" sound is the single most unifying complaint about the XPS 15 and has been cause sufficient for at least a handful of users to return their devices and buy a different product altogether, though others have been perfectly fine with it. Part of the variation in customer reaction could be explained by the fact that the volume of the coil whine varies from unit to unit.
Thus far, Dell has acknowledged the issue and indicated that they are developing a replacement motherboard to fix the issue, which affected customers will be able to obtain at no cost as long as they have an active warranty contract. See the links in the Update at the top of this page for further detail regarding availability of the fix. Until then, it is likely that ordering a new system or requesting a replacement motherboard prior to availability of the fix will leave you with coil whine.
The latest (as of 02 January 2014) claim (among Lenovo users experiencing the same problem on their new laptops) is that the solution is to be found in registry edits that interfere with (or stop) power-state switching by the Haswell CPU. This is possible, but would only help Windows users and would likely result in reductions in battery endurance. However, based on the many comments on the failure of this change to help and the fact that Dell's fix will involve a replacement motherboard, this seems unlikely to be a real solution.
According to a discussion in the user forum at ArsTechnica, the only reason coil whine has become a hot topic is that we've managed to eliminate or reduce the myriad other sounds computers make and only now are we able to hear the sounds caused by high-powered electricals in our computers and distinguish them from the white noise cranked out by cooling fans, spinning hard drives, and optical drives. As such, some users may find relief simply by masking the whine with white noise or music. Heck, maybe it's time to break out the (sound-isolating) headphones and rock out while you get to work.....