Children Eating Well Act or the CHEW Act - Requires each local educational agency (LEA) participating in the school improvement program under part A of title I of the Elementary and Secondary Education Act of 1965 to: (1) develop and implement healthy eating and nutrition education programs in its schools, and (2) periodically monitor schools' efforts to improve students' healthy eating and nutritive knowledge.

Requires LEAs to consult multiple viewpoints in developing and implementing the healthy eating and nutrition education programs.

Includes professional development for teachers, school staff, and food service workers as part of those programs.

Directs the Secretary of Education, Secretary of Agriculture, and Secretary of Health and Human Services (HHS) to establish an inter-agency task force to review nutrition education curricula and recommend effective nutrition education programs for elementary and secondary schools.