New Insurance Coverage Equity (NICE) Act of 1999

New Insurance Coverage Equity (NICE) Act of 1999 - Amends title XVIII (Medicare) of the Social Security Act (SSA) to add a new part D (NICE Drug Benefit Program) (NICE program) (redesigning the current Medicare part D (Miscellaneous Provisions) as Medicare part E (Miscellaneous Provisions) to establish a voluntary NICE program, administered by the NICE Board which also operates a New Insurance Coverage Equity Office established within the Department of Health and Human Services, under which all individuals entitled to Medicare part A (Hospital Insurance) benefits and enrolled in Medicare part B (Supplementary Medical Insurance) shall be provided access to coverage of outpatient prescription drugs that meet specified requirements. Grants such access via either enrollment in a Medicare+Choice (Medicare part C) plan, enrollment in a NICE Medicare supplemental policy, or enrollment in a group health plan, all as defined by this Act. Provides for described financial assistance for covered beneficiaries for them to obtain enrollment coverage, with such assistance varying depending upon beneficiary income. Vests the Board with outreach and other specified duties, such as establishing procedures for enrollment and enhanced financial assistance with regard to eligible Medicare beneficiaries and the NICE program, and conducting certain ongoing studies, as well as a study and report to Congress on permitting an alternative outpatient prescription drug benefit package under Medicare supplemental health insurance policies (Medigap) provisions. Outlines requirements for the offering of NICE program coverage, which include prohibiting pre-existing condition exclusions with respect to coverage and allowing use of reasonable cost containment methods. Establishes in the Treasury the NICE Trust Fund, consisting in part of amounts from the on-budget surplus, to be available only for expenditures to carry out the NICE program. Makes appropriations and authorizes appropriations. Amends the Omnibus Budget Reconciliation Act of 1990 to include with Medigap policy comparison information for Medigap policies, information on the NICE program for purposes of State grant application plans for State-wide health insurance, counseling, and assistance grants.