A fundamental problem in developmental biology is how left-right (LR) asymmetry is generated, both on the whole organism level and at the level of an individual organ or structure. To investigate the relationship of organ sidedness to organ chirality, we examined 12 zebrafish mutants for initial heart tube position and later heart looping direction (chirality). Anomalous initial heart position was found in seven mutants, which also demonstrated loss of normal LR asymmetry in lateral plate mesoderm (LPM) antivin/lefty-1 and Pitx2 expression. Those with a relatively normal notochord (cyc(b16), din, and spt) displayed a predictive correlation between initial heart position and heart chirality, whereas initial heart position and heart chirality were independently randomized in those with a defective notochord (flh, boz, ntl, and mom). The predictability of heart chirality in spt, din, and b16 embryos, even in the absence of normal antivin/lefty-1 and Pitx2 expression, strongly suggests that heart chirality is controlled by a process distinct from that which controls appropriate left-sided LPM expression of antivin-Pitx2 signaling pathway molecules. In addition, there was correlation of initial heart position with gut chirality (and also between heart chirality and gut chirality) in the first class of mutants with normal notochord, but not in the second class, which appears to model human heterotaxy syndrome.