Feature unification in parsing has previously used either inefficient Prolog programs, or LISP programs implementing early pre-WAM Prolog models of unification involving searches of binding lists, and the copying of rules to generate edges: features within rules and edges have traditionally been expressed as lists or functions, with clarity being preferred to speed of processing. As a result, parsing takes about 0·5 seconds for a 7-word sentence. Our earlier work produced an optimised chart parser for a non-unification context-free-grammar that achieved 5 ms parses, with high-ambiguity sentences involving hundreds of edges, using the grammar and sentences from Tomita's work on shift-reduce parsing with multiple stack branches. A parallel logic card design resulted that would speed this by a further factor of at least 17. The current paper extends this parser to treat a much more complex unification grammar with structures, using extensive indexing of rules and edges and the optimisations of top-down filtering and look-ahead, to demonstrate where unification occurs during parsing. Unification in parsing is distinguished from that in Prolog, and four alternative schemes for storing features and performing unification are considered, including the traditional binding-list method and three other methods optimised for speed for which overall unification times are calculated. Parallelisation of unification using cheap logic hardware is considered, and estimates show that unification will negligibly increase the parse time of our parallel parser card. Preliminary results are reported from a prototype serial parser that uses the fourth most efficient unification method, and achieves 7 ms for 7-word sentences, and under 1 s for a 36-word 360-way ambiguous sentence with 10,000 edges, on a conventional workstation.