。
I have a feeling we're going to win.
Literal
Us [subject-が] win-[looks-そう]-[attributive-な] feeling [subject-が] do.
勝ちそう is the observational そう ('looks like X,' attaching to the masu-stem of a verb). The attributive form 勝ちそうな modifies 気 ('feeling'). 気がする ('have a feeling, sense') is the standard expression for intuitive feelings. Literally 'there's a feeling that looks like we'll win' — colloquial for 'I have a hunch we'll win.'