Shoot 'em. Once they realize they can lunch on the chihuahua, they will be back for more.
I live across the street from a 100 foot hill that is a "undeveloped park" (fields). Coyotes are known to be there and I don't feel sorry when people put up their lost kitty signs. The landlord repeats in the monthly newsletter that cats should be house cats and not let run wild.
The same with mountain lions here. If they are seen in town, they shoot them. If they are up in the parks, leave them be. They have been sen within 2 miles of my place.