Here's another possible early chantey reference, which I stumbled on while poking around looking for the journal that Lighter had mentioned.

"Waldie's select circulating library", Volume 1 (12 March 1833)

It's an account of an Italian visitor to London, observing sailors singing in a pub, circa 1826, I believe. Apparently they were singing this idly or for fun. The impression is made that it was a work song. However, it does seem a bit highly developed for that. And the lyrics say "haul," whereas such a long form suggests to me a task like capstan work. It may have been that this was a hauling song, just not a timed-pull one -- i.e. it was a stamp 'n' go. Quite probably these were navy men, as the sentiments suggest.

Here's the first verse.

British sailors have a knack
      Haul way, yeo ho, boys!
Of pulling down a Frenchman's jack,
    'Gainst any odds, you know, boys
Come three to one, right sure am I
If we can't beat 'em, still we try
To make old England's colours fly,
    Haul away, yeo ho boys

The rest can be found here, pg. 133

Haul way, yeo ho