Laughter is a unique expression, essential to affirmative social interactions of humans. Although current 3D talking head generation methods produce convincing verbal articulations, they often fail to capture the vitality and subtleties of laughter and smiles despite their importance in social context. In this paper, we introduce a novel task to generate 3D talking heads capable of both articulate speech and authentic laughter. Our newly curated dataset comprises 2D laughing videos paired with pseudo-annotated and human-validated 3D FLAME parameters and vertices. Given our proposed dataset, we present a strong baseline with a two-stage training scheme: the model first learns to talk and then acquires the ability to express laughter. Extensive experiments demonstrate that our method performs favorably compared to existing approaches in both talking head generation and expressing laughter signals. We further explore potential applications on top of our proposed method for rigging realistic avatars.