let datePredicate = NSPredicate(format: "date == Date()")

// Get the current calendar with local time zone
var calendar = Calendar.current
calendar.timeZone = NSTimeZone.local

// Get today's beginning & end
let dateFrom = calendar.startOfDay(for: Date()) // eg. 2016-10-10 00:00:00
let dateTo = calendar.startOfDay(for: Date(timeIntervalSinceNow: 60*60*24)) // eg. 2016-10-11 00:00:00
// Note: Times are printed in UTC. Depending on where you live it won't print 00:00:00 but it will work with UTC times which can be converted to local time

// Set predicate as date being today's date
let datePredicate = NSPredicate(format: "%@ <= date && date < %@", [dateFrom, dateTo])
fetchRequest.predicate = datePredicate