How is the vacancy filled when the chapter president resigns?

[Guest Faye Robertson]

How is the vacancy of the office of president filled upon the resignation of chapter president?

[jstackpo]

The (first, if you have more than one VP) vice-president instantly becomes the president the moment the (erstwhile) president's resignation is accepted.  RONR, page 575.

If your bylaws have some other rule for succession, the bylaws supersede RONR.