See partial answer above...
Texas law states that a promise to do something must be in writing and signed by the person against whom you want to enforce it.
§ 26.01. PROMISE OR AGREEMENT MUST BE IN WRITING. (a) A promise or agreement described in Subsection (b) of this section is not enforceable unless the promise or agreement, or a memorandum of it, is (1) in writing; and (2) signed by the person to be charged with the promise or agreement or by someone lawfully authorized to sign for him.
(b) Subsection (a) of this section applies to: (1) a promise by an executor or administrator to answer out of his own estate for any debt or damage due from his testator or intestate; (2) a promise by one person to answer for the debt, default, or miscarriage of another person; (3) an agreement made on consideration of marriage or on consideration of nonmarital conjugal cohabitation; (4) a contract for the sale of real estate; (5) a lease of real estate for a term longer than one year; (6) an agreement which is not to be performed within one year from the date of making the agreement;
NOW, look at (6) above as it applies to your situation. Since your employment agreement was to last for 3 years, it needed to be in writing to be enforeable. However, there are exceptions that may apply:
1. An oral contract can be enforced without meeting the requirements of a statute of frauds if the other party admits under oath that the oral contract was made. So, you could sue for breach of an employment contract and if someone that works there testifies that they agreed to bring you on after 3 years, then you may still win.
2. Performance can also prove the existence of an oral contract. This means that one party to the oral contract partially or fully completed his or her duties under the contract. So you can finish your 3 years and then sue for breach.