The Answer:

That quote can be found on the official seal of Kentucky, which was codified in 1792. It is believed that Governor Isaac Shelby adapted it from a line in "The Liberty Song," written in 1768 by John Dickinson. Here's the relevant excerpt:

Then join hand in hand, brave Americans all,
By uniting we stand, by dividing we fall;
In so righteous a cause let us hope to succeed,
For heaven approves of each generous deed.

A later song, George Pope Morris's "The Flag of Our Union," uses the adapted line.

A song for our banner! The watchword recall
Which gave the Republic her station:
United we stand, divided we fall!
It made and preserves us a nation!

(It should be noted that Morris was born in 1802, so his song clearly came after Kentucky adopted the motto.)

—The Fact Monster