Atherosclerosis is characterized by the buildup of arterial plaque. When plaque first begins to form, on which part of the blood vessel do the monocytes bind after taking in cholesterol-rich lipoproteins?

on the smooth endothelial lining

Explanation:

The endothelial lining is the innermost layer  of all cardiovascular system. it serve as the separating barrier between the circulating blood and the inner lining of vascular system. These cells  formed one cell layer thick of capillaries for exchange of nutrients and gases between  the blood  and the needed cells and tissues, also as  lining of  the innermost layers of the heart for diffusion of nutrients to the cardiac cells.

The process of deposit of plaques on the walls of the arteries, which leads to narrowing and hardened of the arteries is called Atherosclerosis.

Monocytes and microphages are attracted to the blood vessels by   the circulating  cytokines and chemokines  from plaque activation . The monocytes  and macrophages bind with  blood vessels, and squeeze their way through to bind with the endothelial lining on the arterial wall to  feed or scavenge on the oxidized low density lipoprotein in  the plaque.  

This  is followed by   corresponding  efflux or release of cholesterol from the macrophages into the endothelial lining increasing the mass of the plaque, aggravating  atherosclerosis.