Does any unifying theory explain why nature is Chiral? I'm currently studying particle physics and find the experimental fact that massless particles are always left-handed quite surprising.In fact, the need to add projectors in the lagrangian seems not very fundamental but rather a pragmatic ad-hoc thing theoretical physicists have come up with.
The question is: Does any current unifying theory explain this asymmetry? Maybe there is a theory where left and right are treated equivalently or, at least, there is an explanation to why left-handed particles are "prefered" by nature.
Or maybe this is just the way the universe works and I just have to get used to it... Anyway, I'd like to know what's the insight on chirality in unifying theories.
 A: I believe Pati-Salam model is what you're looking for.
Quick overview: It is very different from $SU(5)$ unification. The quark-lepton unification is achieved by adding a fourth color labeled "lilac" for leptons, so e.g. electrons are lilac down-quarks. The strong force symmetry group naturally enlarges to $SU(4)$. At the same time, a Pati-Salam partner $SU(2)_R$ for the $SU(2)_L$ field is introduced, which restores chirality.
UPD: Pati-Salam is just one example of a left-right symmetric GUT. Another models also exist, as mentioned by innisfree@.
A: Massless particles are not all left-handed. A photon, for example, has two perfectly good polarisations.
A Dirac fermion can always be written in terms of a left-handed weyl spinor and the complex conjugate of a left handed spinor (which is to say, a right-handed spinor).
It is often convenient to adopt this convention, but that's all it is. The only reason for preferring left over right is that the weak interactions couple to the left-handed particles. This is particularly noticeable for neutrinos (which are not massless). But a right-handed electron exists and has different hypercharge and weak isospin to the left-handed electron to which it is coupled by the Higgs.
A: In the Standard Model (SM) of particle physics, fermions are taken to be left handed. The reason is to incorporate the parity violation in weak interactions. Which is a fact of nature. If one check then in will be seen that $V-A$ type current can account for the inclusion of Left handed fermions ($V+A$ type current may also possible, but its ruled but by experiment). 
Minimal extension of SM is the Left-Right symmetric model, proposed by Rabindra Mohapatra and Goran Senjanovic back late seventies, based on gauge group $SU(2)_{L}\times SU(2)_{R}\times U(1)_{B-L}$. In this model the fermion fields are assigned to the doublets 
$$L_{L}^{i}= \begin{pmatrix}\nu \\ e^- \end{pmatrix}_{L}^{i}\qquad L_{R}^{i}= \begin{pmatrix}\nu \\ e^- \end{pmatrix}_{R}^{i} \qquad Q_{L}^{i}= \begin{pmatrix} u \\ d \end{pmatrix}_{L}^{i} \qquad Q_{R}^{i}= \begin{pmatrix} u \\ d \end{pmatrix}_{R}^{i}$$
It is obvious from the field representations that both left and right handed fermions entered in the game with both hands. The transformation between $L$ and $R$ fields accomplished parity, and impose parity invariance before spontaneous breaking down $U(1)_{e}$.
This model has interesting features and anomaly free, and looks more symmetric compared to SM itself. But despite intense search, no data has found yet supporting this model.
An interesting paper published by Roni Harnik et al recently. Where authors considered the possibility of an universe without weak interactions. They provided theoretical arguments that it is indeed possible to have a stable universe with nucleosynthesis, matter domination, structure formation, in the absence of weak interactions, which is responsible for parity violation. 
A: The theory presented in Schmelzer, I.: A Condensed Matter Interpretation of SM Fermions and Gauge Fields, Found. Phys. vol. 39, 1, p. 73-107  (2009), arXiv:0908.0591, predicts the fermionic sector, the SM gauge group, and its action on the fermions. See http://ilja-schmelzer.de/matter for a popular presentation. 
Given that it predicts the gauge group only as a maximal group fulfilling some assumptions, and the left-right reversed action would be another maximal one, it does not exactly answer the question why the left-handed. It could have been the right-handed as well. But they are above chiral.   
