We propose an objective intelligibility measure (OIM), called the Gammachirp Envelope Similarity Index (GESI), which can predict the speech intelligibility (SI) of simulated hearing loss (HL) sounds for normal hearing (NH) listeners. GESI is an intrusive method that computes the SI metric using the gammachirp filterbank (GCFB), the modulation filterbank, and the extended cosine similarity measure. The unique features of GESI are that i) it reflects the hearing impaired (HI) listener's HL that appears in the audiogram and is caused by active and passive cochlear dysfunction, ii) it provides a single goodness metric, as in the widely used STOI and ESTOI, that can be used immediately to evaluate SE algorithms, and iii) it provides a simple control parameter to accept the level asymmetry of the reference and test sounds and to deal with individual listening conditions and environments. We evaluated GESI and the conventional OIMs, STOI, ESTOI, MBSTOI, and HASPI versions 1 and 2 by using four SI experiments on words of male and female speech sounds in both laboratory and remote environments. GESI was shown to outperform the other OIMs in the evaluations. GESI could be used to improve SE algorithms in assistive listening devices for individual HI listeners.