The first comment on this question was originally posted as an answer. Both statements made are correct and at the level that the question was asked at. Someone pointed out that their are many instances where only one allele is expressed. This is true, obviously, and is quite clearly mentioned in the second sentence. A much more detailed answer could be given and hopefully will be, but that does mean this one should be deleted: the merit of an answer is supposedly decided by voting, not by deleting the ones that people don't like. There is an environment here where people are more concerned with stack exchange rules, real or perceived, than with the actual science, and it's sad. I wonder how discouraging it is to a new user when they are reproved for posting a correct, albeit succinct, answer.
Why was the answer converted to comment:
The statement "This is true for most proteins, ignoring things like imprinting and X-inactivation, which is a bit more advanced to grasp", requires explanation.
The first line of the answer is fine for the title "Which of the two chromosomes in a pair is expressed?" but having touched upon imprinting and not explaining it makes it a comment at best.
Also, "how my cell choose which chromosome, mother's or father's to use to synthesize peptides?" is not actually addressed. I agree that the presupposition is wrong but how the cell uses both chromosomes in most cases could have been addressed.
To sum up, my reason for converting this answer to a comment was that it had insufficient explanation, which IMO is not just against the SE standards but also the common scientific practice.