1. By accident
   - haply [archaic], by luck 
2. Without advance planning
   - accidentally, circumstantially, unexpectedly 
3. [archaic] Through chance, "To sleep, perchance to dream.."
   - perchance [archaic]

Encyclopedia: By chance

• framing
• franc
• franc-tireur
• France
• Frances Eliza Hodgson Burnett
• Frances Elizabeth Caroline Willard
• Frances Hodgson Burnett
• Frances Wright
• Francesco della Rovere
• Francesco Petrarca
• Franche-Comte
• franchise
• franchise tax
• franchisee
• franchiser
• Francis Albert Sinatra
• Francis Bacon
• Francis Beaumont
• Francis Crick
• Francis Drake
• Francis Edgar Stanley
• Francis Everett Townsend
• Francis Ferdinand
• Francis Ford Coppola
• Francis Galton