A growing empirical and theoretical literature argues in favor of specifying monetary policy in the form of Taylor-type interest rate feedback rules. That is, rules whereby the nominal interest rate is set as an increasing function of inflation with a slope greater than one around an intended inflation target. This paper shows that such rules can easily lead to chaotic dynamics. The result is obtained for feedback rules that depend on contemporaneous or expected future inflation. The existence of chaotic dynamics is established analytically and numerically in the context of calibrated economies. The battery of fiscal policies that have recently been advocated for avoiding global indeterminacy induced by Taylor-type interest-rate rules (such as liquidity traps) are shown to be unlikely to provide a remedy for the complex dynamics characterized in this paper.