Most people today would say Harry Carey, but before Harry there was Jack Brickhouse. Also, a legendary broadcaster whose signature call "Hey Hey" appears on the left field foul pole. The Cubs wore a patch with that phrase on it after he passed away in 1998. The same year Harry passed away. Some fans today might even say the Ron Santo is a legendary broadcaster for the Cubs. Granted his legacy is his play on the field and not in the booth, (although his call when Brant Brown dropped an easy fly ball in September 1998 is legendary) but he is definitely a Cubs legend like no other, except maybe Ernie Banks.
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If you mean TV broadcaster, the answer is Jack Brickhouse, who did Cubs games on WGN from 1948 to 1981. If you mean PA announcer, it was Pat Pieper who announced at Wrigley Field from the Cubs' first year there in 1916 through 1974.