Major Robert Edward Chew, according to several genealogies and and obituary, was not the son of John Winslow Chew and Ann Thornton. He was the son of William Lock Chew and Rebecca Freeland. He appears with his father and brother in Mississippi on the 1850 census.

JW and Ann Chew had a son named Robert B Chew, which might have lead to the confusion. But according to an extensive genealogy of the Chew family in america, these two Roberts were no closer than having common 5G grandparents.

I have an image of an obituary for Robert E Chew. Here is a transcription:

February 2, 1863
Memphis Daily Appeal
OBITUARY

Major Robert E. Chew was born in January, 1829 in Adams county, Miss. He was the youngest son of Wm. L. Chew, one of the oldest settlers of the State. Major Chew removed to Memphis several years since, where he practiced law until the commencement of the war. He was among the first to take the field, and as the captain of a company, both at Belmont and Shiloh, proved himself a gallant soldier and true patriot. Upon the reorganization of the army the fortunes of war cast him in the trans-Mississippi district, under Gen. Hindman, where he was immediately placed at the head of the sharpshooters in Hindman's army, with the rank of major. It was while charging at the head of his battalion, at the battle of "Prairie Grove," that he was shot through the heart - thus dying the noble death of the patriot soldier.

The writer of this notice cannot refrain from a passing tribute to the many noble and manly qualities of his deceased friend. His was indeed a character worthy of admiration - brave, generous, high-soulded; modest as a woman in pressing his own advancement, and in the expression of his private sentiments and opinions, but bold and earnest in advocating the entrusts of all his friends. He was a model of excellence among all the young men in his own profession, and unrivaled in all the qualities of the true gentleman. I thought that in social life his virtues shone most conspicuous - there the gentler affections and sympathies of his nature had full and ample play - there he seemed to be more at home even than among the crowd. If but a few know him, those few always respected and cherished him. In the language of one os his oldest and warmest friends, as addressed to the writer: "Few obituary notices could have a better claim upon the generous sympathies of the public, than the one which records the death and merits of this estimable gentleman. In personal qualities he was everything that his friends could desire. He mingled the most unflinching courage with extraordinary mildness and affectionateness of disposition In private intercourse he was distinguished for self-denial and urbanity. His family and friends not only respected but loved him."

Thus has gone one more gallant should to swell the throng of the patriot dead. There in a a far off grave, with the wild grass waving in quiet murmur over the soldier's last resting place, sleeps Chew, the young, the noble, the generous! No monument now marks the silent spot, but soon the hand of affection will trace it out, and all that is earthly will find a fitter burial ground. It is for a grateful country to perpetuate the memory of his many virtues and noble deeds.