A Chance To Serve Act This bill provides various benefits for Peace Corps and AmeriCorps volunteers and increases the number of AmeriCorps volunteer positions to at least 500,000 (currently there are approximately 250,000 positions). Among other provisions, the bill (1) provides eligible former Peace Corps and AmeriCorps volunteers with three years of non-compete eligibility for federal employment whereas currently, former volunteers generally get one year of eligibility with extensions available in certain situations; (2) provides eligible former volunteers with health care benefits for one year; and (3) exempts from taxation certain payments and allowances paid to volunteers.