The show has sort of an odd history. It has impeccable pedigree, written by Betty Comden & Adolph Green, who did the book and lyric, and Jule Styne who wrote the score. Together, they'd written such shows as Bells Are Ringing, and were brought in to collaborate on Peter Pan. Hallelujah, Baby! is largely unknown today, and I suspect is almost never done, but that's where the oddity comes in -- in addition to Leslie Uggams winning Best Actress, the show itself (even though not remembered much today) also won the Tony as Best Musical -- in fact, it won five Tony Awards. However, when the Tony Awards were given out, they had to bring the cast back to perform, because the show had closed. It ran 293 performances -- not dismal, but pretty much a flop...most especially for a Tony-winning show. It has a tuneful score, though a book that didn't work for everyone. (It basically tells the story of Black history.in the 20th century, using the interesting technique of following the exact same characters aging normally, but jumping through the different eras.) But the year the show opened, 1967, wasn't the strongest for Broadway, so a good, though problematic show like Hallelujah, Baby! was able to win.
Here are a couple of numbers with Leslie Uggams from the musical, appearing on The Ed Sullivan Show. The first is her big ballad, "Being Good," followed by the show's title song.