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

• shell jacket
• shell out
• shell parakeet
• shell plating
• shell shock
• shell stitch
• shell suit
• shell-less
• shell-shocked
• shellac
• shellac varnish
• shellac wax
• shellack
• shellbark
• shellbark hickory
• shelled
• sheller
• Shelley
• shellfire
• shellfish
• shellflower
• shelling
• shellproof
• shelly
• Shelta