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

• galleon
• Galleria
• Galleria mellonella
• gallery
• galley
• galley proof
• galley slave
• gallfly
• Gallia
• Galliano
• galliard
• Gallic
• gallic acid
• Gallican
• Gallicanism
• Gallicise
• Gallicism
• Gallicize
• Galliformes
• galligaskins
• gallimaufry
• gallina
• gallinacean
• gallinaceous
• gallinaceous bird