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

• half-and-half dressing
• half-arsed
• half-assed
• half-baked
• half-blooded
• half-bound
• half-bred
• half-breed
• half-caste
• half-century
• half-clothed
• half-cock
• half-crazed
• half-dozen
• half-evergreen
• half-free morel
• half-hardy
• half-heartedly
• half-heartedness
• half-holiday
• half-hour
• half-hourly
• half-intensity
• half-length
• half-life