Test cost is increasingly becoming a major component of a product's design cost in scaled technologies. Exponential increase in test data volumes for sub-45 designs, especially for testing delay faults has led to large increase in ATE cost and test application time. In order to reduce external test cost, Logic BIST has been explored as a possible alternative to manufacturing test [1-5]. However, this paper shows that a large number of faults in BIST logic of large IWLS'05 and ITC'99 benchmark processors remain undetected after BIST run (42% of stuck-at and 34% of transition faults on average) and thus, BIST logic needs to be tested properly. This paper proposes a hierarchical BIST methodology `HBIST' which uses different BIST techniques to obtain complete stuck-at and transition fault coverage of CUT and then introduces additional levels of BIST logic to test for faults in the BIST logic at the preceding levels. A design methodology is proposed to optimize the number of additional levels of BIST required while keeping the BIST area and power overhead, and the addition of extra faults in BIST logic minimal. Experiments on large benchmarks show an average of 95.9% CUT stuck-at fault coverage (ATPG coverage of 96.4%) and 93.5% CUT transition fault coverage (ATPG coverage of 95.3%) is obtained using HBIST. Also, up to 99.2% (average 93.2%) reduction in external ATE test cost (including cost needed to test additional BIST levels) is obtained using two levels of BIST at 7% average area overhead (compared to scan overhead of 38.2%) and 18% increase in test power.