Trow is an archaic word for believe, think, or suppose. The roots of the word trow lie in the Old English word treow (faith, belief).
In Alfred Lord Tennyson's Idylls of the King, Enid's mother shows her a beautiful dress that was stolen years before and then returned. Enid's mother asks if she recognizes it:
See here, my child, how fresh the colours look,
How fast they hold like colours of a shell
That keeps the wear and polish of the wave.
Why not? It never yet was worn, I trow:
Look on it, child, and tell me if ye know it.