As announced in October here, Braun, He, Ovrut, and Pantev have finally found an exact MSSM constructed from heterotic string theory on a specific Calabi-Yau.
By choosing a better gauge bundle - with some novel tricks involving the ideal sheaves - they got rid of the second Higgs doublet. While they use the same Calabi-Yau space with h11=h12=3 i.e. with 6 complex geometric moduli, they now only have 13 (instead of 19) complex bundle moduli.
The probability that this model describes reality is roughly 10450 times bigger than the probability for a generic flux vacuum, for example the vacua that Prof. Susskind uses in his anthropic interview in New Scientist. ;-)