by chance in WordNet English dictionary

1. without advance planning
   "they met accidentally"
   by chance  accidentally  circumstantially  unexpectedly  by chance  accidentally  circumstantially  unexpectedly 
   
2. by accident
   "betrayed by a word haply overheard"
   haply  by chance  by luck  haply  by chance  by luck 
   
3. through chance, "To sleep, perchance to dream.."
   perchance  by chance  perchance  by chance 
   

by chance in English Wiktionary