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

• sezession
• Señor
• Señora
• Señorita
• waitress
• waitron
• waive
• waiver
• Wajda
• Wakashan
• Wakashan language
• wake
• Wake Island
• wake up
• wake-robin
• wake-up call
• wake-up signal
• wakeboard
• wakeful
• wakefulness
• wakeless
• waken
• wakening
• waker
• wakf