it's quite obviously an issue of gear. Or, more correctly, of getting used to your new gear. Been there 
Some mouthpieces tend to be more sensitive than others, although I noticed that chirping is something that can be ligature-dependent as well (one of the few things were a ligature does make a difference in my opinion). But more often, choosing another brand of reed, or another strength, can make a huge difference already.
I notice that even with the same mouthpiece and reed, the amount of chirping depends on which sax I use. My teacher noticed that I had to get used to the speed of the valves of my new sax. I chirped quite a lot, because the octave vent was just a little slower than on my former one. Might be something to look at as well.
Overall advice : fumble a bit with reeds, if no solution, check a ligature, but first of all : get used to the new gear. I do so by starting of slow and increasing the speed of my patterns at every exercise. In the end, you're bound to get the right movements in your fingers to avoid the chirping.
My 2 cents
Some mouthpieces tend to be more sensitive than others, although I noticed that chirping is something that can be ligature-dependent as well (one of the few things were a ligature does make a difference in my opinion). But more often, choosing another brand of reed, or another strength, can make a huge difference already.
I notice that even with the same mouthpiece and reed, the amount of chirping depends on which sax I use. My teacher noticed that I had to get used to the speed of the valves of my new sax. I chirped quite a lot, because the octave vent was just a little slower than on my former one. Might be something to look at as well.
Overall advice : fumble a bit with reeds, if no solution, check a ligature, but first of all : get used to the new gear. I do so by starting of slow and increasing the speed of my patterns at every exercise. In the end, you're bound to get the right movements in your fingers to avoid the chirping.
My 2 cents