[Update: moved.] Located deep in suburban Chiba, Little Zoo has the feel of a neighborhood hangout frequented by a crowd of regulars. The cafe occupies an ordinary house, and has a resident animal population of three falcons (who live in the front yard), more than half a dozen owls (both indoors and outdoors), and various snakes, lizards and turtles that mostly stay in their tanks.
Many of the customers here are bird lovers, and some even bring their own owls to play with the resident birds. (Please consult with the staff before bringing your own bird.) You can drop in for coffee and cake, beers or cocktails in the evening, or a casual meal - their Thai-style green curry (Y1000 with rice and salad) is tasty and quite spicy. There's no cover charge per se but you do need to order something.
If you ask nicely, the staff will let you pet some of the owls. (Note that the staff don't speak English, so brush up on your owl- and reptile-related vocabulary if you need to.)
[Update: Cafe Little Zoo has moved to a new location some distance away; check their website for details.]