The identifying code problem is a special search problem, challenging both from a theoretical and a computational point of view, even for several graphs where other in general hard problems are easy to solve, like bipartite graphs or chordal graphs. Hence, a typical line of attack for this problem is to determine minimum identifying codes of special graphs. In this work we study the problem of determining the cardi-nality of a minimum identifying code in block graphs (that are diamond-free chordal graphs). We present a linear time algorithm for this problem, as a generalization of a linear time algorithm proposed by Auger in 2010 for the case of trees. Thereby, we provide a subclass of chordal graphs for which the identifying code problem can be solved in linear time.