http://grants.nih.gov/grants/guide/pa-files/PA-07-070.htmlThis is for R01, the major funding mechanism of NIH. Her, there is no mention of any nationality at all.
# Eligible Institutions/Organizations. Public/State Controlled Institution of Higher Education; Private Institution of Higher Education; Nonprofit with 501(c)(3) IRS Status (Other than Institution of Higher Education); Nonprofit without 501(c)(3) IRS Status (Other than Institution of Higher Education); Small Business; For-Profit Organization (Other than Small Business); State Government; U.S. Territory or Possession; Indian/Native American Tribal Government (Federally Recognized); Indian/Native American Tribal Government (Other than Federally Recognized); Indian/Native American Tribally Designated Organization; Non-domestic (non-U.S.) Entity (Foreign Organization); Hispanic-serving Institution; Historically Black Colleges and Universities (HBCUs); Tribally Controlled Colleges and Universities (TCCUs); Alaska Native and Native Hawaiian Serving Institutions; Regional Organization; Other(s): Eligible agencies of the Federal government; Faith-based or community based organizations.
# Eligible Project Directors/Principal Investigators (PDs/PIs). Individuals with the skills, knowledge, and resources necessary to carry out the proposed research are invited to work with their institution/organization to develop an application for support. Individuals from underrepresented racial and ethnic groups as well as individuals with disabilities are always encouraged to apply for NIH support.