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

• lurcher
• lure
• lurgy
• lurid
• luridly
• luridness
• lurk
• lurker
• lurking place
• Lusaka
• Lusatian
• Luschka's tonsil
• Luscinia
• Luscinia luscinia
• Luscinia megarhynchos
• luscious
• lusciously
• lusciousness
• lush
• lushly
• lushness
• Lushun
• Lusitania
• Lusitanian
• lust