The first Linux kernels had to be bootstrapped with MINIX, which was developed with a UNIX-like design in mind. Now, Linus used books on UNIX when he was designing his kernel. The date of his book order is even archived.
To this date, Linux is not fully UNIX compatible, therefore, it's designated as "UNIX-Like" (Mac OS X, on the other hand, is a (full) UNIX).
The title of your question states simply "Linux" which implies not only the kernel, but other parts of it as well. I'd argue, that when you take into account things outside the kernel to compare it with UNIX, it is even more alike. Given things like X, etc. The Linux kernel alone comes pretty close to UNIX, but when you take into account the GNU parts, it gets even closer.
The 0.01 version of the kernel, can be still downloaded. Although, I haven't tested whether it compiles, let alone runs.