Step 1:  Create a new document of a suitable size with a default white-filled background. Reset your foreground and background colours to black/white by pressing D on your keyboard.  Then apply Filter > Texture > Stained Glass with the following settings:

Cell Size: 8
Border Thickness: 4
Light Intensity: 3

You should now have a lattice-like texture resembling my one on the left. 

Step 2:  Grab the magic wand tool, and ensure that it is set to a Tolerance of 50, with the Anti-aliased & Contiguous boxes checked.  Now, click on the black lattice so that the whole of the lattice is selected, but none of the white background.  Edit > Cut your selection out, create a new transparent layer, and Edit > Paste it in.   You should now delete the background layer because you don't need it anymore (or, of course, just fill it in with a solid colour and/or texture of your choice).

Nearly there!   To make your lattice resemble chicken wire, just go to Layer > Layer Style > Blending Options and enter the settings on the left into the appropriate sections.  Also apply the 'Bevel & Emboss' style, but leave its settings on Photoshop default.

Step 3:  If a simple wire lattice is your aim, you can just stop now and have a perfectly respectable texture.  If you want something a little bit funkier, though, duplicate the wire layer several times, and move each layer to slightly different positions.  If you do it right, you should end up with an image like the one on the left.   Now, all you have to do to make a decent texture is crop out the centre, and then make it seamless or run the pattern maker.   Enjoy!