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

• sigmoidal
• sigmoidectomy
• sigmoidoscope
• sigmoidoscopy
• Sigmund Freud
• Sigmund Romberg
• sign
• sign away
• sign in
• sign industry
• sign language
• sign manual
• sign of the cross
• sign of the zodiac
• sign off
• sign on
• sign over
• sign painter
• sign up
• signage
• signal
• signal box
• signal caller
• signal detection
• signal fire