Check that your nut is properly adjusted to your strings. If the grooves are too wide, the strings will float and make noise. If you have a Teflon nut, remove it and look below:
1 dot = gauge 9-42 to 9-46
2 dots = gauge 10-52
3 dots = gauge 12-56
Check that your zero fret is not notched. If it is notched, it must be changed. You can buy a replacement from a dealer. If you have the Zero Fret S, you only need to change the individual part of the fret under the string that makes noise.
Install the String Dampener if your guitar didn't come with one stock. Also available from dealers, it sticks just behind the nut and dampens noise.