I recently got a couple tires and an alignment on my 2008, and after I left the shop, I suddenly had a chirping sound. Took it back and they "couldn't hear it." Nor could they "notice anything strange" while driving it, apparently...
You'd think an alignment tech would be able to notice a bad strut, tie rod ends, & sway bar links, but I digress...
Turned out the sound was coming from my strut on the front right. Open up the hood and remove the covers to reveal the top of your strut. Take the cap out and spray some lithium grease (or if you've got some moly grease or wd-40 or whatever you've got) in around the top and between where the strut mounts to the car.
That stopped the chirping sound 100% for me. But the problem was a bad strut, so if this DOES solve your problem, consider replacing it.
Hope that made sense