I'm guessing that you are female, considering that a lot of the old musicals have low guy songs. Don't look at the leads solos in the older musicals. I am unfamiliar with Chitty Chitty Bang Bang. Are the songs in that show high or low? You may want to show off your chest voice, but it wouldn't be prudent if all of the songs are high in that show. Look at Emily Arden's songs from State Fair, Ado Annie in Oklahoma!, Lady Thiang in The King & I and Anne Anderson in Shenandoah. All of Anne's songs are duets, however if you only need a verse and a chorus you can use "Freedom", and "Beautiful Pair" and "Violets and Silver Bells" could easily be solos. I read on another site that this show is very similar to Mary Poppins, so you might want to look at that show as well.
Currently~ Miss Myrna Thorn in Ruthless! the Musical
Recently~ Emma Carew (Jekyll & Hyde), Sister Mary Leo (Nunsense), Demeter (Cats), Tzeitel (Fiddler on the Roof)