Specific heat measurements on the one-dimensional linear chain antiferromagnet TMMC in the temperature range 0.4–4.0 K show an anomaly at 0.83 K indicative of a three-dimensional magnetic phase transition. Above 0.83 K, that part of the specific heat not related to the phase transition, shows a linear and quadratic dependence on temperature in agreement with measurements at higher ( T > 1.5 K) temperatures. The interchain coupling does not appear to be responsible for the observed low value of the linear term. Application of a 15 kG magnetic field along the c-axis broadens the specific heat anomaly and shifts the maximum value from 0.83 K to about 1.0 K.