Chihuahuas in general have kind of bulging eyes, which can cause them to get irritated easily and tear. Them being so low to the ground adds to the issue. Some dogs are more prone to it than others. My last dog was a pug/Jack Russell mix, and he always had goop in the corner of his eyes. My Chihuahua, Gobo, doesn't seem to have the issue as much, maybe because his hair is so short and smooth and the goo doesn't stick. Either way, if it isn't anything new, it probably isn't anything to worry about!
First time Chihuahua owner with many years of dog experience!