Simulations suggest that molecular clock analyses can correctly identify the root of a tree even when the clock assumption is severely violated. Clock-based rooting of phylogenies may be particularly useful when outgroup rooting is problematic. Here, we explore relaxed-clock rooting in the Acer/Dipteronia clade of Sapindaceae, which comprises genera of highly uneven species richness and problematic mutual monophyly. Using an approach that does not presuppose rate autocorrelation between ancestral and descendant branches and hence does not require a rooted a priori topology, we analyzed data from up to seven chloroplast loci for some 50 ingroup species. For comparison, we used midpoint and outgroup rooting and dating methods that rely on rooted input trees, namely penalized likelihood, a Bayesian autocorrelated-rates model, and a strict clock. The chloroplast sequences used here reject a single global substitution rate, and the assumption of autocorrelated rates was also rejected. The root was placed between Acer and Dipteronia by all three rooting methods, albeit with low statistical support. Analyses of Acer diversification with a lineage-through-time plot and different survival models, although sensitive to missing data, suggest a gradual decrease in the average diversification rate. The nine North American species of Acer diverged from their nearest relatives at widely different times: eastern American Acer diverged in the Oligocene and Late Miocene; western American species in the Late Eocene and Mid Miocene; and the Acer core clade, including A. saccharum, dates to the Miocene. Recent diversification in North America is strikingly rare compared to diversification in eastern Asia.