When walking from point to point while in uniform, it is inappropriate and detracts from military smartness for personnel to be smoking or using tobacco products, or to be eating and/or drinking.
The above paragraph is clear on the use of tobacco products while in uniform. However, chewing tobacco should be used in a command-designated area. Most if not all commands have an associated policy that clearly provides guidelines to such usage. When in doubt, please contact your Command Master Chief or Senior Enlisted Leader.
Reference: U.S. Navy Uniform Regulations, Chapter One, Section 1, Article 1101.3.