This is a fantastic question. If you read carefully, there are many allusions to animal-like qualities that describe Lennie. And this is not only in chapter one. As you read, keep following the animal-like allusions. I should say that there is not one particular animal that describes Lennie. Here is an example. Right in the beginning of the book, the first description of Lennie is as follows:
Behind him walked his opposite, a huge man, shapeless of face, with large, pale eyes, and wide, sloping shoulders; and he walked heavily, dragging his feet a little, the way a bear drags his paws. His arms did not swing at his sides, but hung loosely.
Lennie is described as a bear. He moves like a bear, his shape is like a bear, and even his hand are paws. Later on when there is an altercation between the two men, Lennie says that he will go off into a cave if George wants him to do so. This, too, is animal-like.
In the next description of the Lennie, much of the same happens. Lennie and George stop to get a drink of water in the river. Lennie plops down on the riverbank and drinks like a horse. Here is what the text says:
His huge companion dropped his blankets and flung himself down and drank from the surface of the green pool; drank with long gulps, snorting into the water like a horse. The small man stepped nervously beside him.