Habeas Corpus Reform Act of 1991 - Amends the Federal judicial code to set forth special habeas corpus procedures in capital cases. Applies such procedures to Federal habeas corpus cases brought by prisoners in State custody who are subject to a capital sentence. Makes the applicability to such procedures contingent upon a State establishing a mechanism for the appointment, compensation, and payment of reasonable fees and litigation expenses of competent counsel consistent with this Act.

Provides for a mandatory stay of execution during the post-conviction review initiated pursuant to this Act. Details conditions which will cause such stay to expire. Prohibits a Federal court, if one of such conditions has occurred, from entering a stay of execution or granting relief in a capital case unless: (1) the basis for the stay and request for relief is a claim not previously presented by the prisoner in State or Federal courts, and the failure to raise the claim is the result of State action in violation of the Constitution or laws of the United States, is the result of Supreme Court recognition of a new Federal right that is retroactively applicable, or is based on a factual predicate that could not have been discovered through the exercise of reasonable diligence in time to present the claim for State or Federal post-conviction review; and (2) the facts underlying the claim would be sufficient, if proven, to undermine the court's confidence in the jury's determination of guilt on the offense for which the death penalty was imposed, or in the validity of the sentence of death.

Imposes time limits on filing for habeas corpus relief. Requires such time limits to be tolled under specified conditions.

Makes the requirement for a certificate of probable cause inapplicable, with an exception.

States that a mechanism for the provision of counsel services to indigents sufficient to invoke the provisions of this Act shall provide for: (1) counsel to indigents charged with offenses for which capital punishment is sought, who have been sentenced to death and who seek appellate or collateral review in State court, and who have been sentenced to death and who seek certiorari review in the U.S. Supreme Court; and (2) the entry and filing of an order in an appropriate State court of record appointing one or more counsel to represent the prisoner except upon a judicial determination that the prisoner is not indigent or the prisoner knowingly and intelligently waives the appointment of counsel. Prescribes minimum qualifications for appointed counsel. Authorizes payment of fees and expenses for investigative, expert, or other services reasonably necessary for the representation of the defendant. Requires the court to fix the compensation to be paid to an attorney appointed under this Act.