Chip to cause a delay in a pulse
The described function is fulfilled by a digital delay block IC: Several manufacturers offer this, with either fixed or programmable delays, with delay applied to both rising and falling edges or only one edge. To narrow down the search, the desired pulse rate or clock frequency needs to be specified, as well as the extent of delay, minimum and maximum.

One versatile option is the Linear Technology LTC6994-2, which delays both rising and falling edges, by a programmable period from 1 microsecond to 33 seconds. If only one edge is to be delayed, the LTC6994-1 is applicable instead. 

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Both ICs permit adjustment of delay period through a separate analog control voltage.