Chick-a-dee calls of the Mexican Chickadee (Parus sclateri) are composed of combinations of three common note types (A, C and D) and one very rare type (B). Calls have the invariant sequence of notes A-B-C-D, where any note type may be omitted, given once or repeated a variable number of times before transiting to the next type. The B and C notes are phonologically similar to the B and C notes of chick-a-dee calls of the Blackcapped Chickadee (P. atricapillus), but the A note is markedly different and the D note somewhat different from equivalent notes of the congener. A total of 2,071 calls recorded yielded 60 different call types, and Zipf-Mandelbrot plots show that the call system is open; as the sample size is increased new call types will be found without demonstrable bound. In relatively undisturbed contexts (with mate on territory, in fall flocks, alone in fall) birds gave mainly [A][D] calls with lesser numbers of [A] and [C] calls, where brackets indicate variable repetition of note types. In disturbed contexts (mobbing plastic Great Horned Owl, mobbing speaker playing calls of the Northern Pygmy-Owl, observer sitting under the nest cavity) the birds gave more [C] calls with [A][C] as well. In the longest mobbing session to owl calls, birds gave mainly [A] calls when approaching, switched to [C] calls while flying about the speaker, and then resumed [A] calls and moved offwhen the playback was stopped. Outside of human language, this is the second truly combinatorial system of vocal communication found in animals, the first being chick-a-dee calls of the Black-capped Chickadee. This study provides the first data substantiating quantitative differences in calls from different contexts, an important step toward understanding what kinds of information combinatorial chick-a-dee calls encode.