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

• hamate
• hamate bone
• Hamburg
• Hamburg parsley
• hamburger
• hamburger bun
• hamburger roll
• hamburger steak
• hame
• hamelia
• Hamelia erecta
• Hamelia patens
• Hamelin
• Hameln
• Hamilton
• Haminoea
• Hamitic
• Hamitic language
• Hamito-Semitic
• hamlet
• Hammarskjold
• hammer
• hammer and sickle
• hammer in
• hammer nose