I did finally locate a reference which shows where at least "one branch" of the Chilton family was entitled to bear arms:
"Armigerous Ancestors A Catalogue of Sources for the Study of theVisitations of the Heralds in the 16th and 17th Centuries with ReferencedLists of Names", Cecil R. Humphery-Smith, 1997, Section III, p. 171. Index to Pedigrees and Arms: Lincolnshire Chilton, 1550. fo. 86b [N.B. Harleian MSS 1550, Lincoln 1564, 1592]
None of the libraries in my area have the Lincolnshire visitation pedigrees from 1564 or 1592, so I ordered a book on CD from Europe that is supposed to have these manuscripts. I expect to receive the CD sometime in December.