This is taken straight from the 3.5 SRD:
Hide in Plain Sight (Su): A shadowdancer can use the Hide skill even while being observed. As long as she is within 10 feet of some sort of shadow, a shadowdancer can hide herself from view in the open without anything to actually hide behind. She cannot, however, hide in her own shadow.
Now, let's start breaking this down:
A Shadowdancer can use the Hide skill even while being observed.
This is the exception to the main rule for using Hide, which is taken from the 3.5 SRD: "If people are observing you even casually, you cannot Hide." This means that the Supernatural ability of the Shadowdancer allows him to make a Hide check even while under direct observation.
As long as she is within 10 feet of some sort of shadow, a shadowdancer can hide herself from view in the open without anything to actually hide behind. She cannot, however, hide in her own shadow.
The first sentence gives a restriction to the above ability; there must be a shadow of some sort within 10' of the Shadowdancer. The only plausible reason for this is that the shadow must somehow be used for concealment since the SRD quotes, "You need cover or concealment to attempt a Hide check". The second part of that restriction further limits that the Shadowdancer cannot hide in her own shadow. This second part also directly implies that the Shadowdancer has to somehow use this other shadow that is within 10' to hide within and thereby gain enough concealment to make a Hide check.
Now, it has already been established that True Seeing penetrates darkness and magical darkness (and thus shadows, which fall somewhere between visible light and darkness by the very definition of their existence). True Seeing penetrates these forms of concealment and cover of a normal and magical nature (darkness, Blur effects, polymorph, etc). Let's call them optical effects for the sake of simplicity and the desire not to retype the spell description to make my point.
True Seeing has been established that it does not penetrate physical, mundane forms of concealment or cover. A shadow does not have a physical form--it cannot provide cover since it is not a physical thing--so, it can only provide concealment. Although it can be a mundane or magical form of concealment. Nail's misunderstood idea,
True Seeing does not see through all forms of magical "obscuration" (or rather: concealment). Obscuring Mist and Wall of Fire come to mind.
, shall be clarified just in case anyone else is fuzzy on the distinction. Neither Obscuring Mist or Wall of Fire magically obscure anything. They both create physical obstructions. A bank of mist or a wall of fire are physical obscurations (magically created, but physical obscurations nonetheless). Thus, True Seeing would not penetrate them since it is incapable of penetrating physical forms of concealment/cover.
One could argue that the spell description for True Seeing may or may not be conclusive. That is irrelevant. The one common point that the things that the spell can do all share is that they are optical effects. Even polymorph changes the outward appearance from the original but does not block sight from the True Seer to the subject. The common point shared by the list of spell limitations is that they are all physical impediments between the line of sight of the rue Seer and the subject.
Whether you decide to make the list of spell functions and limitations limited to what the book specifically states or take their common points and extrapolate further effects and limitations that would be covered is up to you.
So, if you are going by the very strictest definition of True Seeing, then, no, it does not penetrate Hide In Plain Sight for the only reason that the spell description does not read that it penetrates Hide In Plain Sight. However, if you are one who would rather extrapolate from the examples given (I've already mentioned previously that the writers wouldn't have had the time/space to spell out every example of what the spell can/cannot do and it would be lazy and short-sighted to think otherwise) and decide from there whether or not True Seeing would negate Hide In Plain Sight, then read on:
It's established that:
--Shadowdancers have a supernatural (magical) ability called Hide In Plain Sight to use other shadows within 10' as enough concealment to allow them to make a Hide check even while under direct observation, thus bypassing the main restriction on Hide checks where the subject cannot be directly observed when making a Hide check.
--True Seeing penetrates mundane and magical optical effects, but not physical effects (magical or mundane), that attempt to conceal or cover the true nature or location of the subject being viewed.
--Hide In Plain Sight is a magical optical effect that grants concealment in other shadows sufficiently for the Shadowdancer to make a Hide check even while under direct observation.
Conclusion:
--Since True Seeing negates mundane and magical optical effects, and Hide In Plain Sight is a magical optical effect, the subject wanting to make a Hide check with this ability while under the direct observation of a person actively using True Seeing, cannot make a Hide check since the subject of True Seeing ignores any form of magical or mundane optical concealment that the shadows would otherwise have provided as a necessary requirement of making a Hide check.
All the back and forth about open ended spells, "simply hiding" vs. "hiding", "you're wrong" vs. "no I'm not", and such are missing the issue and seem like arguments just for the sake of arguing while resolving nothing. No one has bothered to elicit a response from any of the PHB authors on this issue and post their decisions here. Until that happens, I'm sticking with this deduction of the True Seeing vs. Hide In Plain Sight issue.