Is being transgender a choice?

It is no more a choice than someone being gay. It is being true to yourself, and learning to be who you are meant to be. Pretty much, you are born the way you are. You will be born trans or gay if you are trans or gay. But it is your choice if you will follow that choice of life or not. You decide if you will accept being trans or gay, or if you will avoid those feelings. The choice is yours.

Another view:
It can be a choice, but it would likely be wrong to say this about all. Most who call themselves transgender tend to be able to be accepted in their original gender role and have little or no discomfort in their original gender role, the one that is consistent with their male or female organs. A number of TG folks are really males (having a penis), if not men (the social role and internal identity) too who simply choose to live as what they are not for any of many reasons. It could be to make a statement, like the attorney who transformed himself into a little girl to point out the absurdity of society's gender roles. Or they could do it because it is popular, they have fetishes, they were taught to hate their own gender, out of closeted gayness, because of sexist beliefs such as women having it easier in the world, or whatever. It could even be done out of an addiction to power by tricking other people, or out of a desire to co-opt women's activities or lead them.

So it is important to see a therapist if you suspect you are transgender or have such leanings. They can help you to clarify what you actually believe and what you are getting from society, peers, family, etc. They can help you to determine if this is a reaction to things in your life or if this is an enduring part of who you are.

Interestingly the path to wholeness, whether you decide to transition or not, is pretty much the same. It all starts with getting to know and accept yourself, making a decision, and getting the information you need for making your decision become reality. Plus it would take accepting, encouraging people.