It's very probably a 200-year-old spelling of chase.
You might find this Sleepy Hollow Glossary helpful, though chace is not mentioned.
Student or Learner
In this sentence (again form "The Legend of Sleepy Hollow"): "As yet the panic of the steed had given his unskillful rider an apparent advantage in the chace, bu just as he..." there is this word "chace". In online dictionaries it is either the baby's name or is being redirected to "chase", which makes perfect sens in the sentence. So if it was really meant to be "chase", was it simply a print mistake or some old-fashioned version of its spelling ?
The OED has citations for 'chace' from the fourteenth to eighteenth centuries.
Reminds me of "shew" in Jane Austen.
1. Thank you for the link to " Sleepy Hollow Glossary"; I'll definitely find it helpful!
2. Where do I get this "citations for 'chace' from the fourteenth to eighteenth centuries" 'cause I entered the mentioned term in search field of "Oxford Dictionaries" online and didn't get any results...
3. So simply speaking it is an old-day equivalent of contemporary "chase", and nothing more, isn't it?