Try the following procedure to measure between two atoms:
1) Click atom1 by left button of mouse with control key.
2) Click atom2 by left button of mouse with control and shift keys.
3) Open the Structure Measurements panel (Tools -> Structure Analysis -> Distances)
4) Click "Create" button to show the distance between the atoms.
5) To deselect atoms, click background with control key.
Unfortunately, UCSF Chimera is not able to mesure distance between groups or group-to-atom. In such case, you can first calculate centroids of groups on the Structure Measurements panel, and do distance between the centroids manually, for instance, using Excel.
You can calculate distance between centroids (for instance, (0.000 0.000 0.000) and (1.000 1.000 1.000)) by sqr{(1.000-0.000)^2 + (1.000-0.000)^2 + (1.000-0.000)^2}.