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Asymmetry is required by most numerical simulations of stellar core-collapse explosions, but the form it takes differs significantly among models. The spatial distribution of radioactive [sup.44]Ti, synthesized in an exploding star near the boundary between material falling back onto the collapsing core and that ejected into the surrounding medium (1), directly probes the explosion asymmetries. Cassiopeia A is a young (2), nearby (3), core-collapse (4) remnant from which [sup.44]Ti emission has previously been detected (5-8) but not imaged. Asymmetries in the explosion have been indirectly inferred from a high ratio of observed [sup.44]Ti emission to estimated [sup.56]Ni emission (9), from optical light echoes (10), and from jet-like features seen in the X-ray (11) and optical (12) ejecta. Here we report spatial maps and spectral properties of the [sup.44]Ti in Cassiopeia A. This may explain the unexpected lack of correlation between the [sup.44]Ti and iron X-ray emission, the latter being visible only in shock-heated material. The observed spatial distribution rules out symmetric explosions even with a high level of convective mixing, as well as highly asymmetric bipolar explosions resulting from a fast-rotating progenitor. Instead, these observations provide strong evidence for the development of low-mode convective instabilities in core-collapse supernovae., Titanium-44 is produced in Si burning in the innermost regions of the material ejected in core-collapse supernovae, in the same processes that produce Fe and [56.sup]Ni (ref. 13). The decay [...]