Question: If a massless observer is going at the speed of light, what speed will it measure of a light beam going parallel to it?

Answer: 
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> what speed will it measure of a light beam going parallel to it ?
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Suppose an entity $A$ has speed $c$ in *an* inertial frame of reference (IFR) then, *according to SR*, $A$ has speed $c$ in *all* IFRs, i.e., there is *no* IFR in which $A$ is at rest.

That is, there are no rulers and there are no clocks at rest with respect to $A$ with which to *measure* distance and time or change of distance with time.

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> The speed of light is always constant so it should be considered as an
>  inertial frame of reference
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There is no IRF with relative speed $c$, there is no IRF in which a photon is at rest, there is no inertial frame of reference for a photon.
It is not possible to attach a reference frame to anything moving at the speed of light. Anything traveling at that speed will not experience any time and will not be able to perform any observations. Thus, it is meaningless to ask about what one would see if he/she traveled at the speed of light.

However, it the observer were traveling at *just below* the speed of light, as always, he/she will also observe light traveling at the speed of light.