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

• perspicuousness
• perspiration
• perspiratory
• perspire
• perspirer
• perspiring
• persuadable
• persuade
• persuader
• persuasible
• persuasion
• persuasive
• persuasively
• persuasiveness
• pert
• pertain
• pertainym
• Perth
• pertinacious
• pertinaciously
• pertinaciousness
• pertinacity
• pertinence
• pertinency
• pertinent