In numerous languages, space provides a productive domain for the expression of time. This paper examines how time-to-space mapping is realized in Yucatec Maya. At the linguistic level, Yucatec Maya has numerous resources to express deictic time, whereas expression of sequential time is highly constrained. Specifically, in gesture, we do not find any metaphorical oriented timeline, but only an opposition between “current time” (mapped on the “here” space) and “remote time” (mapped on the “remote/distant space”). Additionally, past and future are not contrasted. Sequential or deictic time in language and gesture are not conceived as unfolding along a metaphorical oriented line (e.g., left-right or front-back) but as a succession of completed events not spatially organized. Interestingly, although Yucatec Maya speakers preferentially use a geocentric spatial frame of reference (FoR), especially visible in their use of gesture, time is not mapped onto a geocentric axis (e.g., east-west). We argue that, instead of providing a source for time mapping, the use of a spatial geocentric FoR in Yucatec Maya seems to inhibit it. The Yucatec Maya expression of time in language and gesture fits the more general cultural conception of time as cyclic. Experimental results confirmed, to some extent, this non-linear, non-directional conception of time in Yucatec Maya.