Mitrates are a group of stem group Echinoderms, which may be closely related to the hemichordates.

Morphology

The organisms were a few millimetres long. Like the echinoderms, they are covered in armour plates, each of which comprises a single crystal of calcite. However, this is arguably the only feature they share with the latter group; they don't have, for example, fivefold symmetry or a water vascular system.

Their heads had two sides; one, flat, was covered with large "pavement-like" plates, the other, convex, bore smaller plates.
Their tails were long and segmented, resembling the stalk of a crinoid or the arm of a brittlestar. At the opposite end was a hole which may have been mouth or anus - or both.

They also bear features reminiscent of pharyngeal slits, a character lost in echinoderms but present in hemichordates, causing R.P.S. Jefferies to hold them as the ancestor of all chordates

Calcichordate Theory

The Calcichordate Theory holds that each separate lineage of chordate evolved from its own lineage of mitrate, and thus the echinoderms and the chordates are sister groups, with the hemichordates as an out-group....

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Behaviour

Mitrates have been found with associated trace fossils. Their interpretation requires an understanding of how the animal was oriented in life; it's not agreed whether the convex side of the head was up or down, or indeed whether the "tail" was at the front or back of the organism! The trace fossils suggest that they pulled themselves through the mud with their "tail", and were flat-side up.