The Planning Board on Jan. 3 is set to hold a public hearing on four zoning proposals being offered for the Jan. 28 Town Meeting. One of the proposals would allow residents to keep up to six hens on their properties. The town’s zoning rules currently require those who want to keep chickens or any other yard animals on their properties in Burlington to obtain a special permit from the Planning Board. Another article would change how the town regulates land uses that predate zoning rules. A third would amend the definition of “hotel” in the town’s zoning bylaws, and expand where hotels are allowed. The final one would limit access through single-family residential zones to commercial and multifamily zones except over roads in public use. The board is expected to vote on which if any of the proposed articles it will forward to Town Meeting, and what recommendations it will make.