The lake does not have the ability to assimlate the excessive nutrients that are washing in. Two things can help reverse this problem and solve it.
First as mentioned, secure the problem at its root or as Barney from the Andy Griffith show used to say..."Nip it in the bud" I would speak with your neighbors to help eliminate the washing in of the chicken waste.
As that is in the works, secondly add aeration. Aeration as Greg Grimes so well described will allow the lake to degass the harmfull gases like hydrogen sulfide and carbon dioxide while it allows the water that is brought from the bottom to absorb oxygen.
Once the bottom of the lake is aerobic (containing oxygen) it will provide the correct habitat for benificial aerobic bacteria to start tying up those nutritents that are feeding or for lack of better terms fertilizing the algae.
Secondly, by changing the bottom sediments from a negative charge to a positive charge when we aerate, we bond those nitrates and phosphates to the bottom sediments. This also ties up the nutrients so the algae is really hungry now.
Lastly, by circulating the water, the free floating algae cell will be brought down to the lower regions of the lake where the sun light will not be able to help this algae cell to produce chlorophyl (the green color). By combining all four of these elements, you should be very happy with the results.
Make sure if aeration is in your plans that it is sized properly. If a system is undersized, you will have even more of a mess on your hands since it will be lifting those nutrienst into the water column but not satisfying the oxygen demand.
