We present extensive new photometry in (g', i') of the large globular cluster (GC) system around NGC 3311, the central cD galaxy in the Hydra cluster. Our GMOS data cover a 5.5 ' field of view and reach a limiting magnitude i' [?] 26.0, about 0.5 mag fainter than the turnover point of the GC luminosity function. We find that NGC 3311 has a huge population of [?]16,000 GCs, closely similar to the prototypical "high specific frequency" Virgo giant M87. The color-magnitude distribution shows that the metal-poor "blue" GC sequence and the more metal-rich "red" sequence are both present, with nearly equal numbers of clusters. Bimodal fits to the color distributions confirm that the blue sequence shows the same trend of progressively increasing metallicity with GC mass that has previously been found in many other large galaxies; the correlation we find corresponds to a scaling of GC metallicity with mass of Z [?] M0.6. By contrast, the red sequence shows no change of mean metallicity with mass but does show an upward extension to much higher than normal luminosity into the UCD-like range, strengthening the potential connections between massive GCs and UCDs. The GC luminosity function, which we measure down to the turnover point at MI[?] [?] 8.4, also has a normal form like those in other giant ellipticals. Within the Hydra field, another giant elliptical NGC 3309 is sitting just 100 '' from the cD NGC 3311. We use our data to solve simultaneously for the spatial structure and total GC populations of both galaxies. Their specific frequencies are SN(N 3311) = 12.5 +- 1.5 and SN(N 3309) = 0.6 +- 0.4. NGC 3311 is completely dominant and entirely comparable with other cD-type systems such as M87 in Virgo.