In his nearly fourteen years as chief drama critic of The New York Times, Frank Rich was both admired as a passionate advocate for the best in New York theater and reviled as "the Butcher of Broadway" for his presumed destructive power over the commercial fate of Broadway shows. Hot Seat is Rich's definitive chronicle of his long run--an encyclopedic anthology of more than three hundred of his best reviews and essays, interspersed with further thoughts, entirely new to this volume, about his adventures on the aisle at the tumultuous time when Broadway was decimated by AIDS and colonized by the British musical.          Rich's opening-night accounts of an era's biggest hits (from The  Phantom of the Opera to Six Degrees of Separation) and most notorious bombs (from Moose Murders to Carrie) are here, as are his year-by-year reflections on major careers both established (Stephen Sondheim, Peter Brook, Jessica Tandy) and new (August Wilson, Kevin Kline, Caryl Churchill).          Here as well are Rich's final words on his sparring matches with Andrew Lloyd Webber and David Hare, among others, and his retrospective lists of which plays and performances he admired most and least--as well as lists of the productions he feels he over--and underrated the first time around.          From the tragic opening night of David Merrick's 42nd Street to the unprecedented triumph of Tony Kushner's Angels in America, Hot Seat captures what was in every way a dramatic chapter in cultural history, as told and lived by a journalist with the best seat and sharpest eye in the house.