What is the best method to alleviate chronic constipation?

Fluids. Drinking 80-100 ounces of non caffeinated non alcoholic fluid daily will correct most chronic constipation issues in 2-3 weeks, but you have to continue the regimen from that point on.
Hydration. # 1 cause of constipation is dehydration. Increase your fluid intake and fiber intake to bulk and soften stool. A medical evaluation is important too to make sure there are no thyroid or other medical issues. A review of your medication is also important as many medications can cause constipation. Lastly, you may need a colonoscopy to make sure there are no obstructions or masses.