Like most latex displays it is a list and so has \topsep
spacing above it (note thiis is stretchable vertical space not really a blankline) You can set it to 0 eiether inline or in a \newenvironment
definition
\documentclass{article}
\usepackage{alltt}
\begin{document}
xxxxxxxxxxxxxxxxxxxx
{\setlength\topsep{0pt}\begin{alltt}
one two three
four five six
\end{alltt}}%
xxxxxxxxxxxxxxxxxxxxxxx
\end{document}
to redefine alltt
to always do this you can use
\let\oldalltt\alltt
\let\endoldalltt\endalltt
\renewenironment{alltt}{\setlength\topsep{0pt}\oldalltt}{\endoldalltt}