Would a Labrador Retriever and a Chihuahua be compatible with each other?

depends on the dogs…
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with training but the lab could hurt while just playing.
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no chihuahuas dont get along with n e thing
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Yes - they can be compatible - but it really does depend on the individual dog. I would introduce them in a neutral environment to see if they will get along before agreeing to take the Chi.

Labs do have a strong prey drive so be on the look out!
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It depends on the dogs. You could introduce them at a park or somewhere neither are familiar with or consider "their" territory. If they get along, then a visit to your house from the chihuahua would be good. If they still get along, then everything would probably be okay. Does your lab play nice with small dogs? If he doesn't, the biting could be a problem. One bite and he could potentially critically injure the chihuahua. Good Luck!
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Ask your friend to hang on to the Chihuahua until the Lab is completely bite-free. Annoy this dog just like a Chichi will. Pull his tail, pull his ears, grab his mouth, gently push him with your foot, take his food, take his bones, and take his toys. Make sure he is never, ever, ever allowed to bite or even nip, even in play. Chichis have delicate and very thin skin and, while they are fierce in their minds, are in reality quite fragile. And totally defenseless against a big dog's mouth and teeth.

This match is possible! Don't give up! The important thing is to protect the Chichi. Also, make sure to start training her (when you get her) to not annoy your Lab too much. Let them play with ropes and things, but separate them while chewing on bones, eating, or doing anything else that might cause tension.

Lastly, they will both need to sleep in crates. I was once going to get this beautiful little Papillon girl from a breeder. I loved her like anything. One night, while she was still living at the breeder's, one of the Standard Poodles also living there got into the X-pen where she was sleeping with her siblings. The rambunctious Poodle only wanted to play, but she didn't survive. I was heartbroken. Crates will prevent this type of tragedy from happening.
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I hope that these dogs are neutered. You don't want a chihuahua getting pregnant by a lab. The puppies would very likely be too big for her to pass naturally. That was my first thought when you asked about compatibility.
If your lab is having biting issues (is he really biting to be aggressive, or is it just rough play?), they may not be good house mates. My dog is just over a year old (she's a mutt), and she gets a little carried away. But, it's just play. Chihuahuas tend to be a little cocky and snippy (male OR female), so you need to get your lab under control first. Labs are, by nature very gentle and sweet, so it may just be that you may be playing a little too rough with him, and he's not quite in control of how hard to bite on you.
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In a perfect world, we could protect our dogs from negative, anxious and frightening situations. In the real world, we must help our dogs learn how to cope and respond, in a healthy and acceptable manner, to the spectrum of people, animals, places and things they might encounter along the road of life.

By exposing our dogs to different kinds of people, animals and environments, which involves everything from dog obedience classes to vet visits to walks to the park, we can help them develop confidence and ease. This goes a long way in helping them become resilient in the face of unsettling situations.

Further information, http://tr.im/QfSh
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