A long tradition of research has attempted to classify languages rhythmically. Though categorical rhythmic classifications have come under scrutiny in recent years, researchers have found rhythm metrics to be a useful way of discriminating between languages and language varieties, especially varieties of English. However, certain varieties have not been extensively studied, notably Indian English, a variety spoken by tens to hundreds of millions of people. In addition, most of the research has concentrated on read materials, neglecting naturalistic speech. Finally, very few studies consider rhythm within an interaction between speakers and conversational effects of rhythm in this context, including possible convergence between speakers. This paper attempts to contribute to research on rhythm by measuring the rhythm of Indian English as compared to American English in a naturalistic situation of contact between two individual speakers within an interaction. The study yielded strikingly similar results to previous studies on Indian English, showing evidence for syllable-timing in Indian English based on acoustic measurements as compared to previous Indian English data and the current American English data analyzed. In addition, data from different points in the interaction point to rhythmic convergence on the part of the American speaker. This convergence indicates that rhythm is negotiated in the interaction as a conversational device.