The Dictionary Definition of Choose
The American Heritage College Dictionary (3rd edition) defines choose as: to select from a number of possible alternatives.
Dictionary.com defines choose as: to select from a number of possibilities; pick by preference
thefreedictionary.com defines choose as: To select from a number of possible alternatives; decide on and pick out.
The Oxford Compact English Dictionary defines choose as: pick out as being the best of two or more alternatives.
Merriam-Webster's defines choose as: to select freely and after consideration
Encarta World English Dictionary: decide from among range of options
Cambridge Advanced Learner's Dictionary: to decide what you want from a range of things or possibilities:
The Wordsmyth English Dictionary: to select from two or more alternatives.
I could go on, but you get the point.
Why Not Choice?
Choose is an action verb; choice is a noun referring to the completed action. What is special about choosing isn’t the resultant state after the action, but rather the action itself. In choosing one must prefer on alternative to another. While the resultant state is the willing of only one thing; the process of getting to that state involves two things.
On the TV show Smallville, Lex Luther finds one of Clark Kent’s crystals. He has it tested and finds out that it’s made from a special material not found on earth. The question isn't how it coexists with other elements on this planet, but how it got there. Similarly, the verb choose involves twofold possibilities and the noun choice gives the resultant one actuality.
Alternatives and Lowest Common Denominator
Turretinfan provides some definitions of the verb ‘choose’ that don’t use the word possibilities. (link) He thus concludes using a least common denominator method that ‘possibilities’ should “hardly be viewed as the actual "common man" meaning of the term”. The problem is his statement “none of these definitions included the word "possible" or an equivalent concept.” His definitions includes the word “alternatives” which is an equivalent concept. Alternatives are possibilities or things we can choose.
American Heritage Dictionary of the English Language - The choice between two mutually exclusive possibilities.
Encarta World English Dictionary - possibility of choosing: the possibility of choosing between two different things or courses of action
Merriam-Webster's - a proposition or situation offering a choice between two or more things only one of which may be chosen b: an opportunity for deciding between two or more courses or propositions2 a: one of two or more things, courses, or propositions to be chosen b: something which can be chosen instead
Cambridge Advanced Learners Dictionary: something that is different from something else, especially from what is usual, and offering the possibility of choice:
The Wordsmyth English Dictionary - one of two or more possibilities; option.
thefreedictionary.com - The choice between two mutually exclusive possibilities
Dictionary.com - a choice limited to one of two or more possibilities
Oxford Compact English Dictionary - one of two or more available possibilities
Hopefully it's clear that the 'dictionary definition' of choose includes at least two possibilities. But determinism prohibits twofold possibilities, so the dictionary rules out determinism.