No, economists understand that "utility" is ENTIRELY a subjective matter. A given product's "utility" is defined as the value of that product to a specific potential purchaser. Further, the utility to that person is a product of that person's own mind - a complex combination of what the product allows the person to do, how the product makes the person feel, etc.
A chicken's utility depends not just on the caloric content of its meat and eggs, but on how much chicken feed costs in your area, whether you have room for a roost, whether you are a vegetarian, whether you already have more than enough chickens, whether, as a young child, you choked on a chicken bone and thus have an aversion to chicken meat, whether your beloved childhood pet was a chicken, whether your homeowners' association allows livestock, etc.
The "utility" of something to a person is always a function of both factors external to the person and factors internal to the person.
So the demand by that person for a product is a function of all these factors (which determine its utility to that person). This utility determines the price he is willing to pay for each additional chicken. (And his utility changes each time he buys a chicken).
The aggregate effect of individual utilities for individual consumers is what determines the market demand for something. 10 people are willing to pay a million dollars. 1000 people are willing to pay a thousand dollars. 100,000 are willing to pay a hundred dollars. Etc.
Intersect this demand with available supply, and you have the proper price for something. The "cost" is relevant primarily only in that it effects supply. Everyone on the planet is willing to buy one for a penny, but the supply of available chickens for a penny is 0, because no one can make chickens for less than a penny.