Why does my smoke detector chirp even though it has a new battery?

Most devices have battery level algorithms incorporated in the electronics. Since battery levels change so slowly, the algorithm is heavily filtered to reduce the effect of spurious electrical nose or power surges. The filter can be done a number of ways including: software, circuitry, or even something as simple as a resistor-capacitor filter ( a very inexpensive and easy solution). It is likely you unit has that type of level filtering. If you let the battery run down for a long time, or let the device sit idle for hours without a battery it might take the level capacitor a full 15–30 seconds (or longer) to reach the level in the battery. The circuit will wake up as soon as you plug in the new battery but the level will still be reading low so the alarm will beep . No big deal. Consider it a beeper test. In fact, it’s not even worth mentioning in the instructions. You wouldn’t even notice it if you changed the battery as soon as the you heard the first beep.
Congratulations on being so observant. – and for being so diligent about changing the battery .

LuckyGuy Wow GA

Thanks. And in response to a PM…
Think of a battery like a car gas tank and you want an alarm to go off when you reach 10% of capacity. You can put in a float connected to a switched circuit that will beep when you hit that level. Simple and cheap. Except… when you are driving, the fuel is splashing all over the place. Every turn causes fuel to slosh to one side or the other. A panic stop will make the fuel move forward. All of these actions will cause the beep to go off incorrectly. But if you figure a car only burns a maximum off 2 gallons per hour you can filter the signal so the transients are ignored. Look at your car gas gauge and see how slowly it moves. You fill the car up from empty but the gauge does not reach the top until after you drive away.
Your smoke detector has the same sort of filtering. Why? Well, if someone turns on the kitchen microwave that might set it off. The refrigerator motor surge will send a blip whenever it starts. The TV turning on will too. There are all kinds of electrical signals and disturbances around your house. It is best to filter them so you don’t get a false signal in use. If you get one at start-up that is ok. The designer can say it is a “feature” to test the beeper. ;-)

By the way, this is also why you should run your laptop battery down occasionally. We all know it is best for the battery but it is also best for the diagnostic calibration of your PC’s battery level indicator.

Fell free to change the smoke detector battery in whatever manner is convenient for you. Now that you know what’s happening you can experiment and play with it.

I had the same problem. I’ll now put the new battery into the smoke alarm. Thanks @LuckyGuy, I needed that.