James-
Measuring chlorine in water electrically is a bit complicated. It depends on things like the pH of the water. Why you want to quantify the chlorine matters. For example, if you are trying to kill wee beasties in your pool, you are interested in the HOCl (hypochlorous acid).
Anyway, if you measure pH and use an ORP (oxidation/reduction potential) electrode, you can get this kind of measurement.
These electrodes aren't cheap, they are kind of a pain to maintain, and you need to calibrate them.
However...
A pretty good way to measure chlorine is colorimetrically. You might rig some kind of system to suck up a bit of water, then add DPD (N, N-diethyl-p-phenylenediamine), available at pool supply places as solid or in solution. The degree of color change is a function of chlorine concentration.
Then, how to measure? Absorbance of 530nm light is how it is done in some commercial meters. This is a green, and there are LEDs at this wavelength. You could thus
a)get a sample with a little pump controlled by the arduino
b)measure the light that goes through with some sort of light sensor
c)have a device add a few drops of the DPD solution
d)measure again.
You would need to calibrate against either known samples or use a guide published by the maker of the test solution to quantitate.
This is a pretty sensitive test. How you go about getting the water, and adding the reagent, well, that's certainly going to be half the fun. At first blush, it might sound like an ORP electrode is easier, and it might be. Usually, these have both silver and platinum in them, they are often fragile and fussy, and they are expensive.