It sounds like that one particular detector has gone bad.  If all the detectors are wired into each other, they should all go off simultaneously whenever one does  (that way, when there's a fire, all of the alarms will emit so you can become aware no matter which area you're located in).  If only one is "chirping," then it usually means that one detector has gone bad.  (This is, of course, knowing that you have already tried replacing the battery numerous times since they will chirp when the battery has gone dead, too.)  

Go ahead and vacuum out all of your detectors, just in case a spider/insect crawled inside one and set it off  (smoke is made up of particles of unburnt carbon materials and an insect or a lot of dust or large pieces of dust can sometimes break the ionic beam it reads and falsely set the alarm off).  Some people will blow the detectors out with some type of pressurized air too, instead of vacuuming, if they have access to pressurized air (like an air hose for inflating tires- or sometimes firefighters can try holding one of their air bottles up to the alarm and opening the bottle to blow it out,etc).  

You can try "turning off" that specific detector by taking out the battery, but usually that doesn't work as it will chirp/beep the same as if it had a dead battery.  You might be able to find a little square module where the wiring comes into the detector and unplug it from that specific detector, but it depends on the model and how it was wired as to how easy that will be without ruining the wiring for the next detector.