Not so. Your (hypothetical) employee stock agreement, which you were required to sign as a condition of being issued stock options, stipulates that your shares are not transferable, intended for personal investment and not resale, and that your exercise of those options is conditioned on a series of terms that ensures the company can prevent you from selling them.
The reason for this is that your (hypothetical) company isn't trying to create a broad market of investors in its equity. Rather, it's trying to express an incentive that allows employees to share in the upside of a liquidity event at the company.
This issue is distinct from vesting. Even after you've vested, the company is unwilling to yield control of who owns its shares. The company is fine with you parting ways and retaining your upside interest (in fact, it's happy you did!), but not fine with you selling the package that gives you that interest.
For obvious reasons, the story is totally different at public companies.